• Second moment of area moment of inertiaCalculate the second moment of area and radius of gyration of common shapes about weak and strong axes
  • Cubic orientation of primary and shear stresses and principal stress cosine rotationCombine primary and shear stresses into equivalent and principal stresses & their cosines
  • Nucleus and electron shells of atomic elementFind, sort and reorganise the properties of nature's atomic elements with active periodic table
  • Formulas included in Engineering PrinciplesCalculate unknowns in principle engineering formulas: stress, moments, power, energy, capstans, fluids, etc.
  • Properties of a triangle with inscribed and circumscribed circlesCalculate the properties of triangles and triangular configurations including inscribed and circumscribed circles
Area Moment calculation1 Combined Stress calculation2 Elements calculation3 Engineering Principles calculation4 Trigonometry calculation5

Definitions
(technical scientific engineering & mathematical)

High definition values for all constants referred to in this definition page are provided in CalQlata's UniQon calculator.

1-D (line)

A one dimensional shape: a straight line

2-D (plane)

A two dimensional shape: a planar or 'flat' shape that becomes invisible if viewed 'edge-on'

3-D (body)

A three dimensional shape: a shape with volume and mass

Acceleration (a)

Constant rate of change in velocity (velocity ÷ time)

Acid

A corrosive substance at the low end of the pH scale (<7)

Acids turns blue litmus paper pink but does not affect pink litmus paper

The acidic component of water is H⁺. Mix acid with alkaline and the resultant substance tends towards neutral.

Acute (angle)

An angle between 0° and 90°

Added Mass Coefficient
(Ca or Cm)

A coefficient that represents the additional mass of water displaced by a body in which it is immersed:
(0 < Ca < 1)
'additional' means the volume over and above that displaced by the body itself (C = 1.0)

Whilst there are certain circumstances where an added mass coefficient can exceed 1.0, it is a rare occurrence that is invariably due to complex shapes

see Added Drag-technical help
see also Inertia Coefficient and Virtual Mass

Adiabatic
(thermodynamics)

A process that generates a variation in the volume, pressure and/or temperature of a substance, but no heat is added to the system (from outside) or lost to its surroundings (from inside)

see Thermodynamics
see also Polytropic

Aerobe

An organism that can only live in the presence of free oxygen

Aerobic

The breathing (respiration) of free oxygen and its conversion to energy
In earth's animals this means the conversion of oxygen (together with other elements) into water and carbon-dioxide via glycolysis, oxidative decarboxylation and oxidative phosphorylation

Age Hardening

A hardening process that occurs with time with no added chemicals or energy

see also Marageing

Air (the Earth)

The earth's atmosphere is divided into the following layers:
Troposphere
Stratosphere
Mesosphere
Ionosphere (lower Thermosphere)
Exosphere (upper Thermosphere)

99.999622% of the Earth's air (atmosphere) comprises the following gases:
Name (percentage) [ceiling @ equator & poles] {mass}
Nitrogen (78.087%) [3999km & 3458.5km] {4.131E+18kg}
Oxygen (20.95%) [3118km & 2666km] {1.108E+18kg}
Argon (0.93%) [1985.5km & 1647.6km] {4.914E+16kg}
Carbon Dioxide (0.03%) [1525.4km & 1236.4km] {1.585E+15kg}
Neon (0.0018%) [n/a] {9.506E+13kg}
Helium (0.00052%) [n/a] {2.746E+13kg}
Hydrocarbons (0.0002%) [n/a] {1.056E+13kg}
Hydrogen (0.000048%) [n/a] {2.535E+12kg}
Nitrous Oxide (0.00005%) [n/a] {2.638E+12kg}
Ozone (0.000004%) [991.6km & 776km] {n/a}
to which must be added trace elements & about 2% Water

Properties# @ sea level and 273.15K:
Density;
1276.9153g/m³ excluding water
1292.8g/m³ including 2% water
Pressure;
101324.618N/m² excluding water
103351.118N/m² including 2% water
RAM;
28.96376g/mol excluding water
29.3241g/mol including 2% water
# air including 99.99962% of atmospheric gases

see Earth's Atmosphere

Alkaline

A base substance at the high end of the pH scale (>7)

Alkalines turns pink litmus paper blue but does not affect blue litmus paper

The alkaline component of water is OH⁻. Mix alkaline with acid and the resultant substance tends towards neutral

Alloy

An alloy is a compound (mixture) of more than one metal.

A steel alloy normally refers to an iron compound with more than trace amounts of elements other than and in addition to: carbon, manganese, phosphorus and sulphur.

Alpha Iron

Pure iron (< 1,183 K) with a body centre cubic crystal structure will contain up to 0.001% carbon in solution

Alpha Particle

A Helium Nucleus (2 Neutrons and 2 Protons)

The emission of an alpha particle from an atom's nucleus (alpha radiation) will decrease its atomic mass by 4 (or the atomic number by 2)

Alternating Current (AC)

alternating current

Alternating current (and voltage).

Electricity that rises and falls in cycles normally in the form of a 'sine-wave' and normally between Plus and Minus the design current.

AC current is normally supplied by a generator and used for high-power applications (>100W) such as free-standing industrial and domestic equipment.

see also DC (electrical), Apparent Power, True Power, Phase Angle and Power Factor

Ampere (A)

Unit of electrical current.

One Ampere is equal to one coulomb passing through a conductor in one second.

Amplitude

Amplitude

A displacement that represents half the total fluctuation in a complete cycle, or

the maximum deflection of a beam or particle from a central datum

Anaerobic

Respiration that does not use free oxygen to generate energy
E.g. in parasitic flat worms, yeast and occasionally in muscle tissue, all of which break down the respiratory substrates into simpler organic compounds

Angle of Repose (θ)

The smallest angle at which an object will slide down a flat surface under its own weight (or contact force) excluding the effects of stiction, chemistry or magnetism

see Coefficient of Friction

Angular Velocity (ᶜ/s)

The rotational velocity of a body spinning about a central axis, which is measured in radians per second

Anion

A negatively charged ion.

An atom or molecule that has gained excess electron(s) and is therefore attracted to an anode in an electrolyte

Anisotropic

A description of material proproperties that vary with direction, for example:
elasticity, conductivity, permittivity, magnetism, etc. in a single crystal of a crystaline metal, such as; iron, quartz, copper, nickel, salt, etc., and the strength of wood

Anneal
(carbon steel)

To anneal a carbon steel is to soften it.
This process is also referred to as stress relieving.

Forged carbon steel is annealed by heating it to between 500°C and 700°C and holding it at this temperature to allow recrystallisation to occur, followed by artificial cooling.

Cast carbon steel is annealed by heating it above 723°C and holding it at this temperature to allow all the material to transform to austenite, followed by artificial cooling.

Artificial cooling means more slowly than it would cool in still air and is normally carried out in an oven.

Anode

A positively charged electrode that loses cations to a negatively charged electrolyte (corrodes)

Anti-Knocking Agent

The anti-knocking agent used in petrol in most developed countries today is AK-33-X (cyclopentadienyl-Manganese-Tricarbonyl)
Its octane number can be increased by adding a solvent mixture called BTX (Benzene, Toluene and Xylene)

The anti-knocking agent used for petrol in the past was TEL (Tetra-Ethyl-Lead:64%, Ethylene Bromide:25%, Ethylene Chloride:9% and Methylene Dye:2%)

Aphelion

the aphelion of an orbiting planet

The furthest point an orbiting body gets from its attracting mass

Whilst this term can also be used instead of Apogee (i.e. it means the same thing), it is normally used to describe the point at which the distance between sun and its orbiting planet is greatest
This term is made up of the Greek prefix ap for 'away from' or 'farthest point', and helion from 'Helios' the Greek sun god.

a = half the width of the elipse
e = its eccentricity

see also Perigee and Perihelion

Apogee

the apogee of an orbiting planet

The furthest point an orbiting body gets from its attracting mass

Whilst this term can also be used instead of Aphelion (i.e. it means the same thing), it is normally used to describe the point at which the distance between the earth and its orbiting moon is greatest
This term is made up of the Greek prefix ap for 'away from' or 'farthest point', and the Greek word gee for the earth.

a = half the width of the elipse
e = its eccentricity

see also Perigee and Perihelion

Apparent Power (electrical)

Apparent power is the maximum theoretical power of an alternating current (peak current multiplied by peak voltage) and is normally expressed in terms of 'VA' or 'kVA'.

see also AC, True Power, Phase Angle and Power Factor

Arc

A curved line that forms part of the circumference of a circle

Area Moment

A property of the cross-sectional area of any structural body that defines its ability to resist bending or torsion

see also Second Moment of Area, Moment of Inertia and Polar Moment of Inertia

Astroid (curve)

A special case hypocycloid curve

A special case of hypocycloid curve generated by a point on the circumference of a circle rolled around the the inside of a stationary circle four times the diameter without slipping.

see also Hypocycloid

Atmospheric Pressure
(a, atm)

Atmospheric pressure refers to the pressure surrounding your subject or location. The units used for defining pressure above atmospheric are normally given the suffix 'a' or 'atm'

Atmospheric pressure will vary according to the density of the surrounding fluid. At sea-level and on dry land, atmospheric pressure is approximately equal to 14.7psi or 0.1N/mm²
(0 psia or 0 N/mm² [atm])

When quoting or using absolute pressures you must qualify the units with 'a' or 'atm';
e.g. 145psia or 1.1 N/mm²[a]
When quoting pressures over and above atmospheric you should use unqualified units (without 'a' or 'atm') and its abolute value would be 14.7psi greater
e.g. 145psia (1N/mm²[a]) = 159.7psi (1.1N/mm²)

Atom

The smallest constituent part of a substance that comprises all the same atomic elements, which possesses the same properties as the substance in bulk, sometimes referred to as an element

An atom normally comprises any number of protons, neutrons and electrons in roughly equal numbers

Atomic Element

Defined by the number of Protons it has in its nucleus

Atomic Mass Unit
(amu)

One 12ᵗʰ of the mass of a pure carbon atom (¹²C)
1amu = 1.660538921E-24g

One amu is the reciprocal of Avogadro's number

Atomic Number
(Z)

The number of protons in the atom

Austenite

Face centre cubic iron, which occurs at temperatures higher than 723°C (also called Gamma Iron).

At 723°C austenite can absorb up to 0.83% carbon within its crystal structure and hold another 0.87% in solution.
When cooled below 723°C austenite containing 0.83% carbon will form pearlite (eutectoid steel) and the remaining iron and carbon will form ferrite or cementite dependent upon whether the steel contains less or more than 0.83% carbon.

see Carbon Steel

Autoclave

A thick-walled pressure vessel used for heating gases under pressure

Autoclaves are generally used for facilitating chemical reactions that require carefully controlled heat and pressure over a period of time, such as using steam to vulcanise rubber.

Avogadro's Number
(NA)

The number of atoms in 12 grams of pure carbon (¹²C):
NA = 6.02214129E+23/mol

The mole also applies to the same number of any basic component parts; molecules, ions, electrons, etc.

Avogadro's number is also the reciprocal of one atomic mass unit in grammes

Azimuthal Quantum Number (ℓ)

The second in a set of quantum numbers that describes the angular momentum (or shape) of an atomic orbital

The azimuthal quantum number of an electron can only be a positive integer: i.e. 1, 2, 3, 4, 5, 6, 7, etc.

The orbital shape options in any shell are normally identified with the letters; s, p, d, f, etc. Whereas the azimuthal quantum numbers for each shape are defined thus: s(ℓ=1), p(ℓ=2), d(ℓ=3), f(ℓ=4), etc.

At least one other quantum number must be different for each electron in the same shell with the same azimuthal quantum number

Baryon

A family of composite particles made of three quarks which includes protons and neutrons

Baryons are strongly interacting fermions and part of the hadron particle family

Baryon Number

One third of the number of quarks the particle contains

For example:
Any quark is given a Baryon number of ⅓
Any anti-quark is given a Baryon number of -⅓
Protons and neutrons are both given a Baryon number of 1
Anti-protons and anti-neutrons are both given a Baryon number of -1

Basic Oxygen Process

A steel making procedure

It is essentially the same as the Bessemer Converter but blows pure oxygen instead of air through the nozzles.

It produces better quality steel and has largely replaced all Bessemer 'air-blowing' systems.

Bead Wire

A wire approximately 1mm diameter manufactured from 'Plow Steel', which is then drawn down to form the filaments used in wire ropes

The term 'Bead Wire' comes from its use in untreated form to support the rim (or bead) of a tyre

Beam

An elongated body to which a transverse load is applied

Bearing Strength

The ability of a material or a body to support pressure without collapse or plastic deformation

'Bearing Stress' is the measurement designation for this property

see also Stress

Bending Moment

A force applied at a distance that induces bending in a body

Berm

A heap or pile of material (soil, sand, rocks, etc.) normally positioned to protect and/or prevent movement of a structural object (e.g. pipeline)

Bessemer Converter

A steel making furnace

It is a large steel vessel supported on pivots with one spouted opening in the top. Air is blown through a number of nozzles in the flat base to increase applied heat. Oxygen in the air is converted to carbon-dioxide
see also Basic Oxygen Process
Phosphorous is removed from the iron by using an alkali vessel lining, which permitted the wide use of lower quality iron ores in the production of high quality and specialist steels.

This process is gradually being replaced by the Open Hearth furnace

Beta Particle

The transmutation of a neutron into a proton and an electron and the subsequent emission of the electron

In this case, the atomic mass remains the same but the atomic number increases. I.e. the atom changes into a different element

Birdcaging

The term used to describe the unwinding and opening up of a wrapped assembly such as a wire rope or HPHT flexible pipe when it is axially compressed or twisted against the helical lay direction

Bisector

A line that passes through the centre of another line or object thereby dividing it exactly in two

A perpendicular Bisector is a line that passes through the centre of another line or object at right-angles to it

Black-Hole

A collapsed star with sufficient mass to generate the gravitational energy that will prevent photons from escaping its surface

minimum mass: 2.7234E+38 kg
minimum radius for active star that should collapse into a black-hole: 3.5861E+11 m

see Stars & Planets

see also the Sun

Body Centre Cubic (bcc)

body centre cubic

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain nine closely packed atoms, eight of which are located at each corner of a cube and one in its centre.

Boltzmann Constant
(KB)

Defines the amount of energy (Joules) in each molecule of an ideal gas for each degree of temperature (K) relative to absolute zero (K=0)
KB = Rᵢ ÷ NA = 1.38065156E-23J/K per molecule

see also Gas Constant and Avogadro's Number

Bohr Radius
(aₒ)

The radial distance of an electron at ground state (1s) in a hydrogen atom as defined by Nils Bohr
aₒ = 5.2917721067E-11 m

Boson

Any particle that obeys Bose-Einstein statistics

5 are known; Higgs, photon, gluon, W & Z
and
1 is unknown; graviton

Photon, gluon, W & Z are Gauge Bosons

Bosons are normally associated with force and have integer spin properties: 1, 2, 3, 4, 5, etc.

Several bosons with the same energy can occupy the same quantum state, i.e. several bosons can occupy the same place in space.

Bottom Quark

Also known as the beauty quark, it has more than four times the mass of a proton and is part of the third generation of matter

The bottom quark is classified as a fermion

mᵣ=7.451526101E−24g [4.18GeV/c²], lifetime≈1E-12s, Q=-⅓e, Iz=-½

Brass

The term used to describe a copper-zinc alloy

The most common ratios (Cu%:Zn%) are: 95:5, 90:10, 85:15, 80:20, 75:25, 70:30, 65:35 & 60:40
Up to 3% lead (Pb) can be included to improve machinability but this also reduces its structural properties (slightly)

As zinc content rises (see note below):
The following properties increase in magnitude: yield strength, hardness, elongation, thermal coefficient of expansion
The following properties decrease in magnitude: density, melting temperature, thermal conductivity, electrical conductivity

60:40 Brass is known as Munz Metal

Note: this relationship holds true up to about 35% zinc after which the alloy changes phase from alpha brass to alpha-beta brass and strength drops slightly

Bronze

The term normally used to describe copper-tin alloy.
However, bronze is also used to describe copper-aluminium, copper beryllium and copper manganese alloys.

The most common ratios of copper-tin alloys (Cu%:Sn%) are: 98.75:1.25, 95:5, 92:8 & 90:10
Up to 0.4% phosphorus can be added to bronze to improve its castability but this also hardens it

As tin content rises:
The following properties increase in magnitude: yield strength, hardness, elongation, thermal coefficient of expansion
The following properties decrease in magnitude: density, melting temperature, thermal conductivity, electrical conductivity

Brown & Sharpe Taper

A conical shaft and mating sleeve for machine-part self-holding applications that optimises assembly load, holding capacity and easy release (without damage). The tapered shaft is normally driven by an End-Tang (or Key) or a Longitudinal Key.

Different size numbers (0 to 16) relate to different engaged lengths (1-5/16" to 9")

As each size is based upon standard fraction lengths and diameters, not all tapers will have exactly the same taper (angle ≈ 2.4°). The tapers range between 0.04167 and 0.043 inches per inch (2.39° to 2.46°)

The Brown & Sharpe Taper is used for similar applications to the Morse and Jarno Tapers

Bulk Modulus (K)

Relationship between a 2-D stress (load per unit area) and the resultant 3-D strain in a body.

Buoyancy

The vertical (anti-gravity) force exerted by a body immersed in a fluid

A body with a lower density than its surrounding fluid will float or rise (positive force)

A body with the same density than its surrounding fluid will settle mid-column (zero force)

A body with a greater density than its surrounding fluid will sink (negative force)

Capacitance (C)

capacitance lead

Capacitance (the unit of measurement is the 'Farad') is the resistance generated by the storage of Volts as current grows in an AC power supply. This voltage is slowly released as current falls.
It is the retardation of current growth caused by the storage of Volts that creates capacitive resistance.

Current leads voltage

C = Q/V
where: V = voltage, Q = total electric charge

Capstan

A general term used by CalQlata to describe not only a quay-side capstan but any cylindrical surface such as a tree or drum

see Engineering Principles-technical help

Carbide

A binary compound of carbon and a metal
Typical metals that form carbides are: iron, chromium, tungsten, vanadium, molybdenum, titanium and manganese

Carburise

The process of transferring carbon into the surface of a carbon steel to case harden it.

It is carried out by immersing or embedding the steel in a carbon rich substance and heating it to a temperature where the transfer of carbon atoms occurs.

The longer this process is maintained, the greater the depth of hardening.

Cardioid (curve)

A special case epicycloid curve

A special case of epicycloid curve generated by a point on the circumference of a circle rolled around the the outside of a stationary circle exactly the same size without slipping.

Cartesian
Co-Ordinates

Cartesian Co-Ordinates

The definition of a vector using its linear dimensional relationship to the origin of a set of 2-D (x,y) or 3-D (x,y,z) axes

see also Polar Co-Ordinates and Vector

Case Harden

A process during which only the outer skin (or case) of a carbon steel is hardened. The inner body of the material retains its original ductility/toughness.

Cathode

A negatively charged electrode that gains cations via a negatively charged electrolyte (gains matter)

Cation

A positively charged ion.

An atom or molecule with a shortage of electron(s), which is therefore attracted to a cathode in an electrolyte

Cementite (Fe₃C)

A very hard and brittle iron carbide that forms when excess carbon cannot be held in solution in iron

Pure cementite has the following physical properties:
BHN; ≈550
UTS; ≈270ksi
YS; ≈260ksi
elongation; ≈0%

see Carbon Steel

Central Force Motion

Describes the movement of an orbiting body (its deviation from a straight-line path); e.g. a planet towards its sun or a moon towards its planet due to their gravitational attraction.
The force responsible for this motion is 'centripetal'

see also Force Centre

Centre of Buoyancy (CofB)

The centre of mass of the fluid displaced by an immersed body

Centre of Gravity (CofG)

The only point on a line, shape or object that can be supported on the end of a pin without the line, shape or object tilting

(also known as the centre of area or centre of mass)

Centrifugal Acceleration

The positive radial (outward) acceleration of an orbiting body directed away from its centre of rotation (or force centre)

(the opposite of centripetal acceleration)

Centrifugal Force

Centrifugal acceleration of a body multiplied by its mass

(the opposite of centripetal force)

see also Central Force Motion and Force

Centripetal Acceleration

The negative radial (inward) acceleration of an orbiting body directed towards its centre of rotation (or force centre)
e.g. gravitational acceleration is 'centripetal'

(the opposite of centrifugal acceleration)

Centripetal Force

Centripetal acceleration of a body multiplied by its mass

(the opposite of centrifugal force)

see also Gravitational Force, Central Force Motion and Force

CFC

Chlorofluorocarbon - an organic gaseous compound used as a refrigerant and as a pressuriser in aerosol cans.

CFCs have mistakenly been blamed as the cause of a hole in an ozone layer

see Earth-Ozone Layer

Charm Quark

The third most massive of all the quarks and part of the second generation of matter

The charm quark is classified as a fermion

mᵣ=2.299633653E−24g [1.29GeV/c²], Q=⅔e, Iz

Chord

A straight line that joins both ends of an Arc

Circle

A circle is the locus of a point drawn around a single point

The locus generated by rotating a point at a constant distance (R) around a central origin (O)

Where; R² = x² + y²
'a' and 'b' define its centre with respect to a set of co-ordinates and 'x' & 'y' define a point on its circumference with respect to 'a' and 'b'
and like an ellipse: x²/a² + y²/b² = 1
eccentricity = 0

see Elliptical Curves
see also Conic

Clamped End

A fixed support

Coefficient of Expansion (α)

A factor representing the linear relationship between temperature and dimensional change in metals

There are coefficients for;
linear expansion (α): δl = l.α.δṮ
area expansion (α'): δA = A.α'.δṮ
cubic expansion (α"): δV = V.α".δṮ

where
δṮ = the change in temperature
V = volume
A = area
l = length

see Thermodynamics

Coefficient of Friction (μ)

A factor representing the linear relationship between the contact force of two surfaces and their relative sliding resistance
F = μ.W (where F = force required to overcome frictional resistance and W = contact force between surfaces)

μ = the tangent of the Angle of Repose

Column

An elongated body onto which an axial load is applied

Combined Stress (σₑ)

Normally interchangeable with equivalent stress

When differentiating between two different types of combined stress, CalQlata uses the following specific definitions:
Combined stress - the combination of similar types of stress i.e. shear or primary
Equivalent stress - the combination of different types of stress i.e. shear and primary

see also Stress

Compressibility Factor
(gas)

Defines a gas's ability to deform under compression

It is calculated as follows:
Z = P.V ÷ n.Rᵢ.T
Z = p ÷ ρ.Rₐ.T
where:
p = gas pressure
V = volume of gas
ρ = gas density
T = temperature of the gas (abolute)
n = number of moles of gas (mass÷RAM)

See Pipe Flow+ (Fig 1)

Concave

A concave optical lens

A surface that deflects inwards from a flat plane

Convex

A convex optical lens

A surface that deflects outwards from a flat plane

Conductor

A material that allows free movement of its electrons when exposed to a potential difference

This term is relative. You can have a good conductor and a bad conductor. The better the conductor, the easier its electrons flow

see also Resistor

Conic

Elliptical curves cut through a right-circular cone

A curve generated by a plane cutting through a circular cone

The curve is defined by the locus of a point, whose distance from a fixed point (called the focus) is a constant ratio to its distance from a fixed line (called the directrix). This ratio is called the eccentricity (e)

If e = 0 the curve is circular
If e < 1 the curve is elliptical
If e = 1 the curve is parabolic
If e > 1 the curve is hyperbolic

The upper cone is a nappe and the lower cone is another nappe

see Elliptical Curves

Corrosion

Corrosion is the process whereby a metal is degraded and/or its atoms are removed chemically

'Rust' is a special case where oxidisation is the chemical process that occurs in iron via an electrolyte

Coulomb (C)

The unit of electrical charge (or work): 1 C = 1 Amp/sec

One Coulomb is approximately equal to the charge of 6.24150964505573E+18 electrons
where charge = 1 elementary charge unit (e)
i.e.; 1 C = 6.24150964505573E+18 e

The pipeline analogy for Coulomb is the volume of fluid flowing along a pipe

see also Voltage

Coulomb's Law

The force of attraction or repulsion (F) between two charged points is proportional to the product of their charges (Q₁.Q₂) and inversely proportional to the square of their speration distance multiplied by the relative permittivity (d².ε) of the medium:
F ∝ Q₁.Q₂ ÷ d².ε N
where ε is the relative permittivity = εₐ/ε₀
and εₐ = actual permittivity

Coulomb's constant of proportionality (k) changes the above relationship to:
F = k.Q₁.Q₂ ÷ d².ε N

Note: the relative permittivity at atomic level is generally regarded as 1.0
as εₐ is unlikely to vary from that in a vacuum (ε₀), as such; at atomic level...
F ≡ k.Q₁.Q₂ ÷ d² N

Coulomb's Constant
(k)

Charles-Augustin de Coulomb's constant of proportionality for electrostatic force
k = 1 / 4.π.ε₀ = 8.98755178736818E+09 N.m²/C²
where C = Coulombs

see also Coulomb's Law

Covalent Bond

The sharing of pairs of electrons between atoms,

Sharing of paired electrons in covalent bond

which can only occur between electrons in the valence shell (including sub-shells) of atoms

I.e. there must be an electron and a gap in the valence shell of both atoms for bonding to occur.
The number of valence shell 'electron+gap' permutations defines the maximum number of bonds an atom can make

For Example:
Helium has two electrons and no gaps in its outermost shell, therefore it cannot form a covalent bond with another helium atom (2.He ≠ He₂)
Carbon has four electrons and four gaps in its outermost shell and an atomic number of 6:
Its electrons are therefore distributed as follows:
1s² + 2s² + 2p² = 6
Its valence shell contains 4 electrons (2s² + 2p²) and 4 gaps
(2pˉ⁴) that can be shared/paired with 4 other electrons in the valence shell of another atom.
Carbon can therefore generate up to 4 bonds by pulling in four electrons from other atoms to fill its four gaps
e.g.; methane (CH₄) or Ethyne (C₂H₂)
or it can combine with other carbon atoms;
2.C = C₂; 3.C = C₃; 4.C = C₄

Whilst covalent bonds normally occur between non-metal atoms (carbon, hydrogen, oxygen, nitrogen, etc.), they also occur between some metals and non-metals, e.g. beryllium and aluminium both form covalent bonds with chloride atoms.

Creep

The gradual and continual movement or distortion of an object or substance under load over time.

Typical substances susceptible to creep are those will little elasticity such as soils and polymers

Critical Pressure (cp)

The pressure at which a gas will change state to a liquid at its critical temperature. E.g.;
Air: 3.77MPa, Helium: 0.229MPa, Hydrogen: 1.23MPa, Nitrogen: 3.39MPa, Oxygen: 5.04MPa, Carbon Monoxide: 3.499MPa, Carbon Dioxide: 7.397MPa, Ethane: 4.884MPa, Butane: 3.798MPa, Chloroethane: 5.269MPa

Critical Temperature (ct)

Gas: The temperature above which a gas cannot be liquefied by pressure alone. E.g;
Air: 133K, Helium: 5.26K, Hydrogen: 33.26K, Nitrogen: 126K, Oxygen: 154.37K, Carbon Monoxide: 133K, Carbon Dioxide: 304.26K, Ethane: 305.37K, Butane: 426.15K, Chloroethane: 460.37K

Magnets: The temperature (Curie temperature) above which magnets lose their magnetic properties. E.g;
Iron: 1043K, Cobalt: 1400K, Nickel: 631K

Solids: The temperature above which a solid changes state or undergoes a fundamental change of its properties

Crucible Furnace

A Crucible furnace is used to manufacture consistently high-quality steel.

It is a very high-temperature melting process that isolates the steel from the fire in order to ensure total control over the carbon content.
The crucible is a small to medium cylindrical vessel made from fireclay that is sealed with a lid and placed into a fire.

Modern steelmaking methods can achieve almost the same level of quality but much less expensively.

Crystal (metals)

A crystal of any metal is a single body (of any size) containing purely its own atoms (i.e. no impurities) all of which are arranged in prisms (trihedron, quadrahedron, pentahedron, hexahedron, heptahedron, etc.) with the same orientation and spacing in a consistent lattice structure, for example:

body-centre-cubic, face-centre-cubic, hexagonal-close-packed, rhombic, tetrahedral, etc.

As a crystal grows, each face of every prism (or cube) in the lattice structure will also form the face of a neighbouring prism (or cube).

Cubic

cubic

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain eight closely packed atoms, each of which are located at each corner of a cube.

Cubic Expansivity (α")

see Coefficient of Expansion and Thermodynamics

Curie Point

The point at which a material changes to or from being ferromagnetic to paramagnetic or diamagnetic

Some examples are provided below:
Iron: 1,040K
Steel: 1,039K @ C:0.01% to 996K @ C:0.83%
Neodymium: 593K
Cobalt: 1400K
Gadolinium: 292K
Terbium: 237K
Dysprosium: 88K

Current (I)

Is the electrical charge across two points with a potential difference (the unit of measurement is the Ampere). It is the flow of electricity whereby one Ampere is equal to one coulomb flowing in one second.

The pipeline analogy for current is the rate of volumetric flow of the fluid along a pipe

I = V.R
where; R = resistance and V = voltage

Cycle
(thermodynamics)

A 'Process' that returns a heat engine to its original state

Cycloid (curve)

A cycloid curve

A cycloid is a curve generated by a point on the circumference of a circle that is rolled along a flat, straight surface without slipping.

see also Trochoid, Epicycloid and Hypocycloid

Dalton's Law

The pressure of any gas in a mixture is equal to the pressure it would exert if it occupied the same volume alone at the same temperature.

This means that each gas contained in a mixture behaves as though the other gases are not present.
Each gas will expand independently until its pressure is the same everywhere throughout the container but not necessarily the same pressure as any other gas in the container.

The pressure of each gas is called a 'partial pressure'.
You add all the partial pressures together to obtain a total pressure.

Damage Ratio (Ƞ)

Also known as 'utilisation' (the reciprocal of safety factor) is a number that describes the likelihood that a mechanical component or material will survive its design life.

A value of 'one' predicts that the component will fail on the last cycle of its design life with no safety factor. A number less than one reveals a component that will last longer than its design life whilst a number greater than one shows a component that will fail before the end of its design life

Damping (vibration)

The reduction or avoidance of harmonic excitation (resonance).
May be achieved by keeping the operational frequency (ƒ):
ƒ < 0.5 x ƒⁿ
or
ƒ > 1.4 x ƒⁿ

see Vibration Damping-technical help

Damping Factor
(ζ)

The ratio of damping (C) to critical damping (Cc): ζ = C ÷ Cc
also know as a damping ratio

ζ < 1.0 is considered under-damped
ζ = 1.0 is considered fully damped
ζ > 1.0 is considered over-damped

see Vibration Damping-technical help

de Broglie Wavelength
(λ)

The wavelength of a particle due to its momentum

λ = h/p
where:
h = Planck's constant
p = momentum

Deflagration

Sudden burst into flames

see also Explosion

Deformation Energy (Uᴰ)

Energy absorbed/dissipated in the combined deformation of an impacting mass and the impacted system or body

Elastic deformation energy: Uᴰ = ½ky² = ½Fy
{F is the average force: F̌ = 2F and F̂ = 0}

Plastic deformation energy: Uᴰ = Fy {m.a.y}
{F remains constant until momentum ceases}

Where:
k = spring coefficient (see Hooke's law)
y = combined deformation of body and mass
m = mass of body
a = decceleration rate of body on impact

Degrees of Freedom

There are six degrees of freedom; three vectors (or directions) according to the right-hand rule (x,y,z) and three rotations (xy,xz,yz)

On a ship these six degrees of freedom are known as Surge, Sway, Heave and Yaw, Pitch, Roll respectively

Delta Iron

Pure iron (> 1,663 K) with a body centre cubic crystal structure

Density (ρ)

The mass per unit volume of a body or substance, measured in kg/m³, lb/in³ or g/cm³.

e.g. 1.0 m³ of a substance with a density of 3000 kg/m³ will have a mass of 3000 kg.

see also Specific Gravity and Specific Volume

Design Life

The predicted period of time until immediately before a material or mechanical component is no longer expected to comply with its original design specification

Dew-Point
(vapours)

The combined temperature and pressure at which the liquid in a vapour begins to condense

An increase in pressure and/or a reduction in temperature of the vapour will cause this to occur

Dezincification

The removal of zinc from an alloy due to corrosion or heat
The result of which is to reduce its effective percentage quantity in the alloy along with its beneficial effects

Diamagnetism

The repulsion of a non-magnetic material from a magnet
(magnetic repulsion tends to be weak)

Dirac's Constant (ħ)

ħ = h ÷ 2π = 1.05457207144921E-34 J.s
where: h = Planck's constant

Direct Current (DC)

Direct current

Steady-state current (and voltage) that does not vary in cycles (see AC).

DC current is normally supplied by battery and used for low-power applications (<100W) such as mobile phones, computers and hand-held tools.

DC generators are also used for DC power supply but much less frequently (than for AC power).

Disorder
(thermodynamics)

A measure of randomness in the molecules that compirise a system (e.g. gas, liquid, solid, etc.)

Randomness, and hence disorder, increases as molecules move further apart and/or move out of alignment, such as in crystaline arrangements, which occurs due to an increase in temperature and/or through decay.

see also System, Crystal (metals) and Entropy

Distributed Load

Also known as a line load, is applied (not necessarily equally) to a body along a line (not necessarily straight) and denoted as a load per unit length

Down Quark

One of the two types of quark that make the proton and the neutron and forms part of the first generation of matter

The down quark is classified as a fermion

mᵣ=8.538949767E-27g [4.79MeV/c²], Q=-⅓e, Iz=-½

Drag Coefficient (Cd)

A coefficient that represents the resistance between a fluid and a surface over which it is passing and with which it is in contact

For example, a theoretically perfectly smooth surface will have no resistance due to drag (zero), however, this scenario is fictitious as there is no such thing as a perfectly smooth surface

Relatively smooth surfaces and low profiles will have a low drag coefficient (< 0.7) whilst rougher surfaces and high profiles will exhibit higher drag coefficients (> 0.7)

Whilst there are certain circumstances where a drag coefficient can exceed 1.0, it is a rare occurrence

see Added Drag-technical help

Draw

The process of reducing the diameter of a filament (single or individual metal wire) by pulling it through a small die

Duplex (stainless steel)

A stainless steel containing approximately equal proportions of Ferrite and Martensite

Dynamic Amplification Factor (DAF)

A factor by which a force (or weight) is multiplied in order to account for the dynamic nature of its condition

e.g. F = mass x g x DAF

E = m.c²
(Henri Poincaré)

Relativistic momentum

Why isn’t E = ½.m.c² ?

E² = m².c⁴ + p².c² = m².c⁴ + m².v².c² = [m².c²].c² + [m².v²].c²
E²/c² = m².c² + m².v²
[momentum at light speed]² + [momentum at actual speed]²
and because mass at light speed is zero,
momentum at light speed = 0

Therefore at velocities less than that of light:
E²/c² = m².v² [momentum at actual speed]²
E² = m².v².c²
E = m.v.c (relativistic momentum)
and Poincaré's formula looks like this:
E = m.v.c
which, at light speed looks like this:
E = m.c²

see also Momentum

Earth (properties)

Diameter @ poles: 12713.504km
Diameter @ equator: 12756.274km
Surface area: 5.09493884932169E+08km²
Volume: 1.0832072662532E+12km³
Mass: 5.9665854161E+24kg
Density (average): 5508.2583kg/m³
Distance from the Sun:
minimum: 1.471E+08 km
mean: 1.496E+08 km
maximum: 1.521E+08 km

The earth's principal constituent materials are:
Rock 1.86856E+24 kg
Iron 3.41777E+24 kg
Nickel 4.22241E+23 kg
sulphur, silicon, carbon, etc. 2.58011E+23 kg

see Earth's Properties and Earth's Atmosphere
see also Air (the Earth)

Elastic Moduli

Describes the two and three-dimensional behaviour of materials under elastic deformation and includes: shear, bulk and Young's moduli along with Poisson's ratio

Elastic Strain

A material that returns to its pre-deformation dimensions when stress is released
(i.e. obeys Hooke's Law)

Elastic Stress

A load per unit area that is less than the material's yield stress

see also Elastic Strain

Electric Furnace

The Electric Furnace is a process for melting steel.

It uses high current electricity to melt the steel. It can be combined with the Bessemer Converter and Open Hearth methods by dipping charged electrodes into the melt.

This process is capable of very high volume production and good quality control. It is also relatively inexpensive

Electrode

An electrical conductor (solid metal) that can transfer ions to or from an electrolyte

Electrolyte

A positive or negative electrically charged liquid that conducts electricity through ionisation.

Seawater is a predominantly negatively charged electrolyte that will Corrode relatively positively charged metals (e.g. aluminium and zinc) and plate (coat) relatively negatively charged metals (e.g. carbon steel and tin) if immersed together. However, because water molecules are polar (they have both positive and negative probes), immersed steel will corrode in the absence of a donor material (e.g. aluminium or zinc)

Electro-Motive Force (emf)

The work done to move electrons by an electrical force (emf) across a material with electrical resistance. Whilst 'emf' and potential difference ('pd') are normally differentiated, they are essentially the same, as are their units of measurement (Volt)

Electron

A negatively charged particle that normally orbits the nucleus of an atom
m=9.1093897E-028g [0.510998913MeV/c²], lifetime>4.6E+26yrs, Q=1e, Rad=9.087345835484E-17m, Iz

Electron Affinity

The energy required to remove an electron from a negative ion

Electronegativity

A tendency for collecting electrons

These numbers (between 1 and 4), as defined by Pauling, are used to determine the contribution an element will make to an ionic or covalent bond

The higher the Electronegativity, the more electrons it will collect

Electron Shell(s)
(and sub-shells)

Shells are numbered 1 to 7 (in the periodic table)
Sub-Shells are allocated letters: s, p, d, & f

The numbers of electrons in each shell are as follows:
s = 2; p = 6; d = 10; f = 14 (irrespective of the shell)

Shell 1: s₂ = 2
Shell 2: s₂ p₆ = 8
Shell 3: s₂ p₆ d₁₀ = 18
Shell 4: s₂ p₆ d₁₀ f₁₄ = 32
Shell 5: s₂ p₆ d₁₀ f₁₄ = 32 (Uranium)
Shell 6: s₂ p₆ d₁₀ f₁₄ = 32
Shell 7: s₂ p₆ d₁₀ f₁₄ = 32

In theory; after filling sub-shell f, shell number 5 should create another sub-shell but 'f' represents the limiting force-field
All atoms above 5f (Uranium) are unstable; a very short half-life (the greater the atomic number the shorter the half-life).

Electron Volt
(eV)

The energy received by the charge of an electron due to the potential difference of 1 Volt
1eV = 1.60217648753E-19 Coulomb

see also Elementary Charge Unit

Element
(structures)

A bar, beam, plate or member that constitutes part of a larger structure but which can be analysed individually

Elementary Charge Unit (e)

The negative charge (-Q) carried by a single electron or the positive charge (+Q) carried by a single proton

1 elementary charge unit [Coulombs] =
       Faraday's constant ÷ Avogadro's constant
       (1e = 1.60217648753E-19C)

see UniQon

see also Electron Volt

Elementary Particle

The fundamental particles of matter.
All elementary particles are either fermions or bosons

Fermions
Quarks: up, down, top, bottom, strange, charm
Leptons: electron, electron neutrino, muon, muon neutrino, tauon, tauon neutrino
Bosons
Higgs, graviton
Gauge Bosons: photon, gluon, W, Z

Ellipse

An ellipse is the perimeter of a slanted section through a cylinder

The circumference of a flat section cut at any angle through a right-circular cylinder

where; x²/a² + y²/b² = 1
eccentricity = √(1 - (b/a)² ) < 1

see Elliptical Curves
see also Conic

End Cap (force)

A longitudinal tensile or compressive force in a pipe wall as a result of a variation in temperature and/or pressure

see also Upheaval Buckling

Energy (U)

Essentially the same as work with the same units

Energy sources can be mechanical, electrical, chemical or thermal

There are three principle forms of mechanical energy:
Potential (Uᴾ)
Kinetic (Uᴷ)
Deformation (Uᴰ)

There are four principle forms of thermodynamic energy:
Entropy (S)
Internal (U)
Heat (Q)
Work (W)
see Thermodynamics

There are a number of atomic-nuclear energies, four of which are:
Fusion
Fission
Gravitational
Relativistic momentum

Enthalpy (H)
(thermodynamics)

The total energy of a system
H = U + Ṯ.Cp
H = U + p.V + Uᴷ + Uᴾ + ...
where;
U = internal energy
R = gas constant
Cp = heat capacity
Ṯ = temperature (absolute)
Uᴷ + Uᴾ + ... = pressure, Kinetic, Potential, magnetic, chemical, gravitational, etc. energies

The units of measurement are J, Btu, W.s, N.m, lbf.ft, etc.

see Thermodynamics
see also Energy and Specific Enthalpy

Entropy (S)

The measure of disorder in a system defined by energy that cannot be converted into work

Entropy is only a measure of disorder;
it is not a measure of temperature
temperature simply affects entropy
To explain ...

Entropy is the basic level of energy inherent in all molecules that is defined by the following formula:
KB x Ln(N) {per molecule}
where KB = Boltzmann constant & N = molecule microstate
which is true for all molecules even at absolute zero
Note: 'N' varies with temperature, therefore entropy varies with temperature

Temperature increases as heat energy is added to the above basic level. The temperature of any substance is defined by its gas constant (Rₐ) and limited by its heat capacity (cv). Therefore, as a substance gains or loses temperature (heat energy) its entropy will be affected due to its molecules moving further apart, thereby increasing disorder.

So:
the second law of thermodynamics remains true in that entropy (disorder) always increases with time through natural and inevitable decay (irrespective of temperature)
and
the third law of thermodynamics also remains true in that; as temperature decreases molecules pack closer together reducing their disorder, thereby reducing entropy

Process formulas for a change in entropy such as:
δs = cp.Ln(Ṯ₂/Ṯ₁) & δs = cv.Ln(Ṯ₂/Ṯ₁)
are temperature dependent, and:
δs = Rₐ.Ln(V₂/V₁)
is a direct calculation of disorder (variation in volume)
making them consistent with the above because δs is a measure of change in disorder, and all these formulas define this change due either to a variation in temperature or volume.

see Heat Capacity and Thermodynamics
see also Boltzmann Constant, Gas Constant, Specific Entropy and Disorder

Epicycloid (curve)

An epicycloid curve

An epicycloid is a curve generated by a point on the circumference of a circle that is rolled around the outside of another circle without slipping.
A curve generated by a point on the same circle but not on the circumference is called a 'Epitrochoid'.

Special Case: The path generated by a point on the circumference of a rolling circle with the same radius as the stationary circle will be a 'Cardioid'.

see also Cycloid, Trochoid and Hypocycloid

Epitrochoid (curve)

see Epicycloid

Equilateral (triangle)

A triangle with all three sides of equal length

Equilibrium

A state of constancy, stability and balance

Equilibrium applies to mechanical, chemical, electrical and thermal systems that may be transferring energy but the exchange is constant, i.e. unchanging

Equilibrium Diagram

see also Phase Diagram

Equivalent Stress (σₑ)

Normally interchangeable with combined stress

When differentiating between two different types of combined stress, CalQlata uses the following specific definitions:
Combined stress - the combination of similar types of stress i.e. shear or primary
Equivalent stress - the combination of different types of stress i.e. shear and primary

see also Stress

Escape Altitude

The altitude at which gravitational acceleration of a body (e.g. planet, star, etc.) is equal to the centrifugal acceleration due to the orbital velocity (v²/r) of a satellite holding a constant position over the body
Where 'v' is the linear velocity of the orbiting body and 'r' is the distance between the centres of mass

This altitude for the earth is 35843425.4809m above sea level.

see also Geosynchronous Orbit

Euclidian Geometry

A universal method of geometric calculation (developed by the Greek mathematician Euclid 323 BC - 285 BC) based upon a few basic rules.
I.e. once a few basic rules have been established, they can be used to determine a multitude of other related (and even unrelated) mathematical problems.

see Newton's Laws of Motion.

Eutectic

A mixture of two metals that are completely soluble in a molten state but completely insoluble in a solid state. As the liquid cools to form a solid, alternate layers of each pure metal will form in the crystal(s) creating a laminated structure (like plywood).

Eutectoid

A mixture of two metals in a solid state that are completely soluble at a high temperature but completely insoluble at a lower temperature. As the material cools to form a different lattice structure (e.g. the transition of iron with 0.83% carbon from austenite above 723°C to pearlite below 723°C), alternate layers of each pure metal (or ferrite in steel) will form in the crystal(s) creating a laminated structure (like plywood).

Exosphere

Stratum of the earth's atmosphere that constitutes its outer limit (Ionosphere to 1000km)

Contains neutrons and protons that have been detached by the sun's electromagnetic radiation

Temperature increases exponentially with increasing altitude

Explosion

Sudden release of energy, that is usually chemical but it can also be pressure
(i.e. energy = pressure x volume)

An explosion is always accompanied by an increase in heat and sometimes by deflagration.

Face Centre Cubic (fcc)

face centre cubic

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain fourteen closely packed atoms, eight of which are located at each corner of a cube and one in the middle of each face of the cube.

Farad
(F)

The unit of electrostatic capacitance that when charged by the potential diference of 1 volt carries a charge of 1 Coulomb

Faraday's Constant
(F)

The magnitude of electric charge per mole of electrons
1 F = 96485.3317942158 C/mol {exact}
(F = NA . e)
where C = Coulomb

Fatigue

The deterioration of a material due to repeated stress cycling

see Fatigue-technical help

Fatigue Life

The total number of stress cycles (sum of all stress blocks) that represent the expected life of a material or mechanical component and above which damage or failure will occur

Fermion

Any particle that obeys Fermi-Dirac statistics

Fermions include sub-atomic particles; leptons and quarks and compound particles; neutrons and protons

Fermions have half integer spin properties: ½, 1½, 2½, 3½, 4½, 5½, etc.

see also Pauli's Exclusion Principle

Ferrite

Body centre cubic iron, which can absorb up to 0.006% carbon within its crystal structure at room temperature and up to a maximum of 0.03% carbon at 723°C (also called alpha iron)

Pure ferrite has the following physical properties:
BHN; ≈90
UTS; ≈46ksi
YS; ≈36ksi
elongation; ≈30%

see Carbon Steel

Ferromagnetism

The ability of a magnetic material to retain its magnetism
(permanent magnet)

Filament

A single very thin wire or cord of any cross-sectional shape that normally forms part of a multi-filament construction, e.g. a strand

see also Wire Rope

Fire-Point

A temperature above which a substance will give off sufficient vapour to maintain combustion

This temperature is usually higher than the Flash-Point for the same substance

see also Flash-Point

Fission

The splitting of an atomic element into two or more smaller particles (e.g. a helium atom into two hydrogen atoms), which releases energy

Fire a neutron at a nucleus. The nucleus will split apart into lighter nuclei (smaller elements), thereby releasing unnecessary Neutrons. These Neutrons will impact other nuclei, splitting them into smaller elements and releasing more Neutrons (ad infinitum), and thereby causing a chain reaction.

Fixed Support

A support that prevents all six degrees of freedom

Flammable

Having the ability to catch fire under certain conditions

see also Inflammable

Flash-Point

A temperature above which a vapour from a substance will combust if exposed to a spark or small flame

It is usual to define this value on the basis of test using a Cleveland cup or Penskey-Martens apparatus

This temperature is usually lower than the Fire-Point for the same substance

Flexural Modulus

The deformation stress behaviour associated with polymers
The plastic equivalent of Young's modulus

Fluid

A liquid or a gas

Focal Length
(of a lens)

Focal length of an optical lens

The distance along the axis of a lens between a principal plane (at its axis) and its nearest focal point.
This distance (ƒ) is identical both sides of the same lens.

see also Power (of a lens)

Focal Point
(of a lens)

Focal points of an optical lens

The theoretical point (F) of intersection between the axis of a Lens and an exiting light-ray that entered the lens parallel to its axis at a radial distance of almost zero.

The primary focal point occurs at the front of a lens
The secondary focal point occurs at the back of a lens

Force (F)

A load applied by an accelerating body (mass) on another body (mass), that may be stationary or in motion, thus changing their states of motion

There are a number of specially applied forces, such as:
Weight
Impressed Force:
a force exerted on a body in order to alter its state
Centripetal Force:
an attracting force between masses causing them to move towards each other; Fᵖ = m.a
Centrifugal Force:
a force causing a body to recede from its orbit according to the following relationship; Fᶠ = ½.m.v² / r
Gravitational Force:
also called weight and centripetal force; Fᶢ = m.g

Force = mass multiplied by acceleration (F = m.a)

Force Centre

A mass or force maintaining an orbiting body (mass) in its orbit, e.g. the force centre of any solar system is its sun, and the force centre of a bolas is the tension it its tie-cord(s).
The force exerted by a force centre is 'centripetal'

see also Central Force Motion

Free Cutting Steel

Free cutting steel is plain carbon steel with good machinability

Plain carbon steel with more than 0.2% carbon is relatively difficult to machine because of its hardness and its embedded manganese increases this hardness.

Sulphur is added to plain carbon steel to improve machinability, which it does by combining with the manganese to create manganese sulphide. This compound ensures clean chip separation without brittle fracture during machining.

Free Support

A support that allows all six degrees of freedom

Frequency (ƒ)

The number of times a cyclic event is completed in a given time period. A frequency of a number of cycles each 'second' is measured in 'Hz'.
For example; a frequency of 6 cycles a second is equal to 6 Hz. Its reciprocal (1/ƒ) is the time taken to complete one cycle (¹⁄₆th of second) i.e. the cyclic 'period'

The higher the frequency (i.e. the shorter the wavelength) the greater the energy in the wave

The natural frequency (ƒⁿ) of an object is the frequency at which it can regenerate a complete cycle itself (free oscillation) with minimal external assistance and is dependent upon the elasticity and inertia in the system.
Natural period is the reciprocal of natural frequency (1/ƒⁿ)

Freeze

The conversion of a liquid to a solid

Friction

Friction is the resistance to relative movement between two surfaces

see also Stiction and Coefficient of Friction

Frustum

A pyramid truncated by a flat plane normal to its axis

Fulcrum

The point about which a lever or moment couple rotates

Also called a pivot point

Fusion

The conversion of a solid to a liquid, which absorbs energy (the opposite of freeze)

Also used to describe the joining of elements (e.g. two hydrogen atoms to make one helium atom), which releases energy

Galileo's
Laws of Motion

Inertia: Every object persists in its state of rest, or uniform motion (in a straight line); unless, it is compelled to change that state, by forces impressed on it (Newton's first law)

Falling Objects: The distance traveled by a falling body is directly proportional to the square of the time it takes to fall

Uniform motion: d ∝ t

Uniform Acceleration: v ∝ t

Parabolic Curve: A projectile that with a uniform horizontal and a naturally accelerated vertical motion describes a path which is a semi-parabola (i.e. half of a full parabolic curve)

Terminal Velocity: A body falling from a very considerable height will reach a velocity that will remain constant due to frictional resistance from the surrounding air (see CalQlata's Fluid Forces calculator)

Frame of Reference: Any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments

see Laws of Motion

Galvanic Corrosion

Describes the form of corrosion whereby a sacrificial metal (anode) will lose material (protons) to another metal (cathode)

Whilst this phenomenon normally occurs due to both metals being immersed (or wetted) by a common liquid (an electrolyte) facilitating the electrical transfer of positively charged ions from one to the another, it can occur if both metals are joined by any similarly capable medium.

The electrical property responsible for this phenomenon in metals is Electronegativity, which indicates their relative nobility

Gamma Iron

Pure iron (> 1,183 K) with a face centre cubic crystal structure holds up to 2% carbon in solution

Gamma Radiation

The emission of very short-wave electromagnetic energy from the atom's nucleus
No particles are emitted during Gamma radiation

Gamma radiation often occurs during the production of alpha or beta radiation

λ < 1.0E-11m (ʄ > 2.99792459E+19Hz), Q=1.2483E+05eV

Gas

A substance in a state whereby all of its atoms (or molecules) repel each other
and occupies a variable volume and a variable shape

The natural state for a gas is to fill its container, within the constraints of gravitational attraction

This state occurs at high relative temperatures for all substances

Gas Constant (R)

The energy required to raise the temperature of an ideal gas by one degree

Universal (ideal) constant for all gases {per mole}:
Rᵢ = NA.KB = 8.314478766579 {e.g. J/K/mol}

Specific (mass) gas constant {per unit mass}:
Rₐ = Rᵢ/RAM = cp - cv {e.g. J/K/g}

Gas constant {for total mass of gas}:
R = Rᵢ x moles = Rₐ x mass {e.g. J/K}

see Heat Capacity, Thermodynamics and Steam (properties)
see also Boltzmann's constant and Specific Heat(s)

Gas:Oil Ratio

The volumetric (e.g. ft³ or m³) ratio of oil to gas at 1 atmosphere and 60°F

Gauge Boson

Bosonic particles that act as carriers of the fundamental forces of nature

General Relativity

Newtonial physics ...
that applies to the laws of gravity and motion of objects moving significanly less than the speed of light
excluding the effects of time

see also Special Relativity

Generator

A generator is a motor that acts in reverse

Copper wire coils are rotated within the field of magnets. This rotation (which is applied externally) produces an electrical current in the wire coils, which feeds AC or DC electrical power supplies.

Geosynchronous Orbit

The altitude where the gravitational acceleration of a planet/star equals the centrifugal acceleration on an orbitting satellite that remains continuously over exactly the same spot on the planet.

R = ³√(G.m/ω²)
where:
R = geosynchronous orbital radius from centre of planet;
G = gravitational constant;
m = mass of force centre
ω = rotary velocity of planet (ᶜ/s)

Increased speed at this altitude will result in the centrifugal acceleration being greater than gravitational acceleration causing the satellite to drift out into space.
Reduced speed at this altitude will result in the centrifugal acceleration being less than gravitational acceleration causing the satellite to fall back towards the surface of the planet.

see also Escape Altitude

Gluon

A strong force-carrying gauge boson or messenger particle

Gluons are elementary expressions of quark interaction and indirectly involved with the binding of protons and neutrons together in atomic nuclei

There are 8 types (or colour) of gluon, any combination of two from the following colours:
red, anti-red, green, anti-green, blue and anti-blue
whilst the above range theoretically allows 9 colour combinations, there are in fact only 8!
This is because gluons naturally exist in pairs and if all pairs are full their would be no means whereby colour can be transferred (i.e. the voids {the lone or single gluons} allow the transfer of gluons between gluon pairs)

A gluon is a Gauge Boson

m=0g, Ø≈10ˉ¹⁵m, lifetime>10²⁹yrs, Q=0, Iz=1

Golden Ratio
(Φ)

A universal ratio found in nature and mathematics which was first used by Phidias (500 BC - 432 BC; after whom the value is named)
e.g. it was demonstrated by Euclid to be the ratio with which the diagonals of the regular pentagon cut each other

Φ-1 = 1/Φ
using quadratics becomes: 1 + ½(√5-1)
and equals: 1.61803398874989

Grain (crystal)

A complete single crystal of similar atoms in the form of a naturally occurring lattice structure

A grain of any material can also contain atoms of a different type but these atoms must be small enough to fit into the gaps (spaces) within the crystalline lattice structure of the granulated material

Grain growth produces in large (coarse) grain structures resulting brittle metals
Small (refined) grain structures produce more ductile metals

Gravitational Acceleration (g)

Where it is necessary for CalQlata to impose a default value for 'g' in any of its calculators (e.g. UniQon), the value used is; 9.80663139027614 m/s² (which happens to be at latitude 45.5° {Milan or Minneapolis}). The reason for selecting this figure is as follows:

a) ISO states that; 1lb (force) = 4.448222N (exact)

b) ISO also states that; 1lb (mass) = 0.45359327kg (exact)

c) The above defaulted value for 'g' appears if you divide; 1lb (force) by 1lb (mass)
{4.448222 ÷ 0.45359327}

d) CalQlata default's to the above value for consistency between its calculators and this website

The imperial equivalent for the above 'exact' value for 'g' is 32.173987500906ft/s²

CalQlata's UniQon-technical help includes a facility for calculating an accurate value for 'g' (at your latitude) should you require one.

see Earth's Properties

Gravitational Constant (G)

A universal constant that defines the gravitational attraction (force) between two or more bodies

There are a number of estimates for this value (N.m²/kg²):
Newton: 6.67E-11 (estimate)
Cavendish: 6.76E-11 (estimated from his experimental results)
Nature: 6.67191E-11 (10th Jan 2014)
Quinn: 6.67545E-11 (experimental)
Shawn Halayka: 6.671282E-11
Std value: 6.67384E-11
CODATA: 6.67408E-11

Until an accurate value can be established, CalQlata has adopted; G = 6.67128190396304E-11
as it appears to provide the best fit for all our calculations
(see 'Laws of Motion')

The above units (N.m²/kg²) are the same as (m/s²)² / (J/m³)
which is acceleration squared per unit energy density
The Imperial equivalent of which is;
G = 1.068637E-09 ft³/lb/s²

'G' can be calculated from the following known properties of any accurately specified sphere ...
the density of the material (ρ)
gravitational acceleration of the mass at its surface; 'r' (g)
... and the following formula:
G = g ÷ 4/3.π.ρ.r
For example; using the earth as our mass (≈sphere):
ρ = 5508.2583kg/m³
r = 6371000.685m (volumetric radius @ sea level)
g = 9.80663139027614m/s² (@ sea-level & latitude 45.5°)
G = 9.80663139 ÷ (4/3.π x 5508.2583 x 6371000.685)
   = 6.671281904E-11m³/kg/s²

see also Specific Volume and Gravitational Constant

Gravitational Constant (gc)

A dimensionless conversion constant for gravitational acceleration used in calculations dependent upon their units
SI units: gc = 1.0
Imperial units: gc = 32.173987500906

Gravitational Energy)

The energy in a mass that attracts other masses towards it

E = m.g.R
where g is the gravitational acceleration of mass (m) at radius (R)

CalQlata refers to the limiting gravitational energy as that in which;
g.R = c²
where c is the speed of light in a vacuum

Gravitational Force (Fg)

A centripetal force acting between two or more bodies that is a function of their combined mass and the distance(s) between them according to the following relationship:
Fg = G.m₁.m₂ / r²
where G is the Gravitational Constant

Graviton

Is a hypothetical gravitational force carrying gauge boson

It is not yet known if it exists

m=0g (at rest), Ø≈0m, lifetime=∞, Q=0, Iz=2

Guided Support

A support that allows four degrees of freedom; lateral movement in both planes, axial movement and axial twist

Hadron

Is a bound state of quarks, which includes protons and neutrons

There are two hadron sub-sets; baryons & mesons

Half Life

The time required for half the radioactive material to decay

Example:
Bismuth (Bi²¹⁴) → Thallium (Th²¹⁰) + Alpha decay (5 day half-life)
Fraction remaining = 1/2ⁿ where n = the number of half lives or the number of 5 day periods (remaining)

Head (liquids)

The height of the surface of a liquid above a specified datum

Heat Capacity
(Cp and Cv)

The quantity of heat energy that can be absorbed by a given mass of substance per degree (temperature)
This value varies with temperature

Cp = m.cp
Cv = m.cv
where;
cv = specific heat capacity (constant volume)
cp = specific heat capacity (constant pressure)
m = mass

The units of measurement are J/K, Btu/°R, W.s/K, N.m/K, lbf.ft/°R, etc.

see Heat Capacity
see also Ratio of Specific Heats

Heat Energy (Q)

The quantity of heat (energy) in a system at atmospheric pressure

Q = Ṯ.Cp
where;
Cp = heat capacity
Ṯ = temperature (absolute)

The units of measurement are J, Btu, W.s, N.m, lbf.ft, etc.

see Heat Capacity and Thermodynamics
see also Specific Heat Capacity

Heat Transfer Coefficient
(U, h)

The rate at which heat flows through a material or substance of specified thickness.
Also known as 'Thermal Conductance'

Heat Transfer Rate (q)

The rate at which heat flows from a material or substance of unit volume.

Heave (vessels)

Heave

The linear movement of a vessel in the direction of the vertical ('z') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Helical Gear

A gear wheel, with teeth cut into its circumference in the form of a helix, that mates with another helical gear wheel

The tooth profile is similar to that of a spur gear tooth

The centres of rotation of two mating helical gear wheels are not necessarily parallel

Henry
(H)

The unit of mutual inductance such that...
the emf of one Volt induced in a circuit at one Ampere per second

Hexagonal Close Packed (hcp)

hexagonal close packed

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain twelve closely packed atoms, all of which are located at each corner of an hexagonal prism. This is the most closely packed of all the lattice structures.

Heisenberg's Uncertainty Principle

see Uncertainty Principle

Higgs Particle

The Higgs particle is a very unstable boson with no spin, electric charge or color charge that almost immediately decays into other particles.

It is a carrier of the Higgs field, which is supposed to give everything a mass component and without which all particles would simply be energy packets flying about at the speed of light.

m≈2.246153801E-25g [≈126GeV/c²], Iz=0

Hooke's Law

States that stress and consequent strain obey a linear relationship and that dimensional recovery is total when the material is relaxed

This law applies to any elastically deforming body (e.g. a spring, a steel body, rubber band, etc.) all of which have a unique spring constant ('k') that defines the force needed to deform the body by one unit of length
The units of measurement for 'k' are Force ÷ Distance {e.g. N/m or lbf/ft}

see also Young's modulus

Hoop Stress

Primary circumferential stress in a pipe or cylinder

Hydrocarbons

Molecules comprising only hydrogen and carbon atoms

Predominantly organic fluids (liquids and gases) originating from degraded and compressed animal and/or vegetable matter

Includes; glycol, glycerine, benzene, propane, methane, ethylene, toluene, etc.

Hyperbola

An hyperbola

The perimeter of any vertical plane through two inverted right-circular cones

where; x²/a² - y²/b² = 1
eccentricity = √(1 + (b/a)² ) > 1

see Elliptical Curves
see also Conic

Hyper-Eutectoid

A mixture of two metals that exist above their eutectoid state

For example, an hyper-eutectoid steel is a mixture of pearlite and cementite; i.e. solid iron with > 0.83% carbon below 723°C

Hypocycloid (curve)

An hypocycloid curve

A hypocycloid is a curve generated by a point on the circumference of a circle that is rolled around the inside of another circle without slipping.
A curve generated by a point on the same circle but not on the circumference is called a 'Hypotrochoid'.

Special Cases:
The path generated by a point on the circumference of a rolling circle with ...
... half the radius of the stationary circle will be a straight line.
... a quarter the radius of the stationary circle is an 'Astroid'.

see also Trochoid, Epicycloid and Cycloid

Hypo-Eutectoid

A mixture of two metals that exist below their eutectoid state

For example, an hypo-eutectoid steel is a mixture of pearlite and ferrite; i.e. solid iron with < 0.83% carbon below 723°C

Hypotenuse

The side opposite the 90° angle of a right-angle triangle

Hypotrochoid (curve)

see Hypocycloid

Hysteresis

hysteresis loop

A loop showing a delay in the recovery of one property that varies as a result of varying another.

A complete hysteresis loop is one where recovery catches up in each cycle (as shown in diagram).

Ideal Gas

A gas, the molecules of which, are of negligible size and do not interact chemically with each other

For example: nitrogen, argon, carbon dioxide, oxygen (O₂) and air are all ideal gases
oxygen atoms (O) and ozone (O₂) are not ideal gases

Also called a perfect gas

Impedance (Z)

Impedance is the total electrical resistance in a conductor

Impedance² = Reactance² + Resistance²

Inductance (L)

inductance lead

Inductance (the unit of measurement is the 'henry') is the resistance generated by the induced (or 'back') emf (electro-motive force), which opposes the applied emf and therefore retards the growth of an AC current
It is this retardation of current flow by the induced emf that creates inductive resistance.

Current lags voltage

V = L.δI/dt
where: V = voltage, I = current and t = time

Inertia

A body's resistance to a change in state of motion, which is a function of its mass
Inertia is measured in units of mass, e.g. kg, lb, etc.

Inertia Coefficient (Ci)

A coefficient that represents the 'Added Mass' plus the mass of fluid displaced by the body itself

Also known as Virtual Mass

Inflammable

In its strictest sense this means the inability to catch fire under any conditions, however, it is frequently used as an alternative for 'Flammable'
CalQlata use this word to explain 'the inability to catch fire under any conditions' in the same way as incapacity means the inability to perform.

see also Flammable

Internal Energy (U)

The energy in a system that has not been supplied from its surroundings

In a static system: U = Ṯ.Cv
In a dynamic system: U = Ṯ.Cv + ½m.v²
where;
Cv = heat capacity (constant volume)
Ṯ = temperature (absolute)
m = mass
v = velocity

The units of measurement are J, Btu, etc.

see Heat Capacity and Thermodynamics
see also Specific Internal Energy

Involute (curve)

An involute is the curve generated by unwinding (straightening out) the arc (or circumference) of a curved shape such as a circle. For example: the end of a cotton thread unwound from a reel and pulled tight (straight) will describe a curve of ever-increasing radius as the unwound length of thread gets longer.

involute curve of a circle

The figure shows the involute of a circle, which can, for example, be represented by the path generated by the end of the a thread as it is unwound from a reel. The circumferencial length of arc ('A-O') is equal to the straightened out (unwound and tightened) length 'A-P'.

The radius of the involute curve at any point is equal to the arc length of the circumference unwound. For example in the figure, the radius of the curve at 'P' is equal to the straight length 'A-P', which is also equal to the curved length 'A-O'.

Involute curves are almost always used for the profile of gear teeth for the following reasons:
1) Mating teeth always share the load whilst engaged
2) Relative rates of motion between engaged teeth are constant and uniform
3) The line of action between teeth is always the tangent of a circle and therefore always acting perpendicular to the tooth surface
4) 1 to 3 above mean minimum wear and maximum load carrying capacity

Ion

The number of orbiting electrons in an atomic element relative to the number of protons in its nucleus

A positive Ion has fewer electrons than protons. A negative Ion has more electrons than protons

Ionic Bond

Ionic bonding [only] involves the complete transfer of valence electron(s) between metal and non-metal atoms.
The metal atom loses electrons to become positively charged (cation).
The non-metal atom gains those electrons to become negatively charged (anion).
These opposite electrical charges are what subsequently holds these atoms together.
For example: Na + Cl → Na⁺.Clˉ = Sodium & Chloride (salt)

The greater the electrical polarity of each atom the greater the strength of the bond.

Ionic bonds are generally stronger than covalent bonds. But bonds such as those in diamond (carbon) prove the exception is also true.

Ionisation Energy

This term is used to describe the various energies required to isolate and attach sub-atomic particles, atoms and molecules

The term in CalQlata's Elements database refers specifically to the energy(ies) required to remove an electron(s) from an atom

Ionosphere

Stratum of the earth's atmosphere that contains only atoms and light ions of nitrogen and oxygen (Mesosphere to 600km)

Temperature increases with increasing altitude

Isentropic
(thermodynamics)

A process during which no change in entropy occurs
i.e. whilst the temperature of a gas may change during a process, the heat energy (Q) available to do work remains the same;
excess heat energy in a rising temperature process may be lost to the surroundings or other parts of the process, or;
sufficient heat energy is recovered or added to a falling temperature process to maintain a constant amount available for work

see Thermodynamics
see also Polytropic

Isobaric
(thermodynamics)

A process during which there is no change in pressure
I.e. whilst the volume and/or temperature of a gas in a system may vary, no resultant change in pressure will occur

Isobaric refers only to the pressure properties of a process, it is therefore possible for a process to be isobaric and isochoric and/or isothermal

see Thermodynamics

Isochoric
(thermodynamics)

A process during which there is no change in volume
I.e. whilst pressure and/or temperature of a gas in a system may vary, no resultant change in volume will occur

Isochoric refers only to the volume properties of a process, it is therefore possible for a process to be isochoric and isobaric and/or isothermal

see Thermodynamics

Isosceles (triangle)

A triangle with two of its sides of equal length and therefore, two equal angles

Isothermal
(thermodynamics)

A process during which there is no change in temperature
I.e. whilst pressure and/or volume of a gas in a system may vary, no resultant change in temperature will occur

Isothermal refers only to the temperature properties of a process, it is therefore possible for a process to be isothermal and isobaric and/or isochoric

see Thermodynamics

Isotope

Defined by the number of neutrons, relative to the number of protons, in the nucleus of an atomic element

For example: Uranium 238 (U²³⁸) is an Isotope of Uranium (there are also 235, 236, etc. Isotopes of Uranium) but U²³⁸ is the most common
U²³⁸ has 92 protons and 146 neutrons

Isotropic

A description of material proproperties that do not vary with direction, for example;
the pressure in static fluid and elasticity, conductivity, permittivity, such as; in amorphous or multi-crystal materials e.g. steel, alloys, rock, plastic, rubber, glass, etc.

Independent Wire Rope Centre

A multi-stranded wire rope in which the core is an individual strand and not a fiber or polymer or single filament

Jarno Taper

A conical shaft and mating sleeve for machine-part self-holding applications that optimises assembly load, holding capacity and easy release (without damage). The tapered shaft is normally driven by an End-Tang (or Key) or a Longitudinal Key.

You can have any size you like, but each taper is described dimensionally as follows, for example:

Taper No. 7
Length=7÷2", Large Diameter = 7÷8",
Small Diameter = 7÷10"

Taper No. 12.35
Length=12.35÷2", Large Diameter = 12.35÷8",
Small Diameter = 12.35÷10"
etc.

All tapers have a slope of 0.6 inches per foot (2.86419236832929°)

The Jarno Taper is almost a direct alternative to the Morse Taper and used for similar applications to the Brown & Sharpe Taper

Joule

A measure of energy named after James Prescott Joule, who developed the theory of heat

1 Joule is the amount of energy expended by moving ...
... a force of 1 Newton over a distance of 1 metre
or
... an electric charge of 1 Coulomb through a potential difference of 1 Volt

Kepler's
Laws of Motion

1ˢᵗ An orbiting body follows the path of an ellipse

2ⁿᵈ Any two (or more) equal areas of elliptical orbits will be swept by equal periods of time

3ʳᵈ The square of the period of motion is proportional to the cube of the orbital semi-major axis

see CalQlata's elliptical curves calculator and Laws of Motion

Kinetic Energy (Uᴷ)

Energy possessed by a moving body

Linear: Uᴷ = ½mv² ÷ gc

Rotational: Uᴷ = ½Iω² ÷ gc

Where:
v = velocity of the body
ω = rotational velocity (ᶜ/s)
m = mass of body
I = moment of inertia
gc = gravitational constant (dimensionless)

Laminar Flow

A fluid that flows perfectly smoothly generating no disturbance or mixing of adjacent layers

Lang Lay

A particular type of helical lay pattern in a wire rope where the filaments are wrapped within each strand in the same helical direction as the strands are wrapped within the wire rope. In a manufactured wire rope, the filaments run at an angle (diagonal) to the long axis of the wire rope (see image).

 Lang Lay

You can have 'right Lang lay' or 'left Lang lay' configurations:
In a 'right Lang lay' configuration the strands follow the same helical direction as a right-hand screw thread
(see image)
In a 'left Lang lay' configuration the strands follow the same helical direction as a left-hand screw thread
(opposite to image)

Lang lay wire ropes provide excellent wear resistance when used with a sheave (or pulley) due to their smoother (flatter) surface and high bending fatigue resistance but suffer from birdcaging if ill used.

They are generally used for specialist applications where repeated bending and wear resistance is an issue but structural stability is not.

see also Regular Lay

Latent Heat

The heat required to change a substance from one state to another with no resultant change in temperature

For example; latent heat of vaporisation is the heat required to convert a liquid into a gas

Lateral Stress

Primary stress at right-angles to the axis of a component

Latitude (Lat)

The horizontal grid-lines that divide the surface of the earth into 180 unequal spherical segment zones (slices)

The vertical distance between each gridline at the equator = 111319.8922m
The vertical distance between each gridline at the poles = 110963.0597m
The surface area between two gridlines at the equator (0° & ±1°) = 4.46094E+12m²
The surface area between two gridlines at the poles (±89° & ±90°) = 7.7361644E+10m²

Lattice Structure
(metals)

General term encompassing various specialised patterned structures of metal atoms in a crystal in their lowest energy state.

see also Body Centre Cubic, Face Centre Cubic, Hexagonal Close Packed and Tetra-Hedra

Latus Rectum

The latus rectum of an elliptical curve

The width of an elliptical curve (2p) at its focus (F)

Also called the parameter of the curve

see also Ellipse, Hyperbola and Parabola

Lens

An optical lens

A device that converges electromagnetic waves (radiation) at a focal point#

A lens may converge or diverge the radiation dependent upon the path of the light-ray in relation to the convex or concave nature of the lens faces.

The front of the lens is the face at which the radiation enters the lens
The back of the lens is the face at which the radiation exits the lens

# The generally accepted position of the focal point of a spherical lens is theoretical (see Focal Length).

Lepton

A family of sub-atomic particles within the fermion group

There are 6 leptons (Iz isospin quantum number);
electron(-½) & electron neutrino(½)
muon(-½) & muon neutrino(½)
tauon(-½) & tauon neutrino(½)

Lift Coefficient (Cʟ)

A coefficient used to define the lateral force (or lift) developed in a beam or structure as a result of a fluid passing along or across it at 90° to the direction of lift

This coefficient varies between 0 and 4, and is dependent upon the Keulegan-Carpenter number,
which must be 0 > Kc > 130 for lift to occur
Maximum lift force occurs when Kc ≈ 12

Light (visible)

That which is visible to mankind

Ranges from: ultra-violet > infra-red
1.0E-08m < λ < 0.001m
(2.99792459E+16Hz > ʄ > 2.99792459E+11Hz)

The speed of light (c) in free-space (a vacuum) is defined as:
c² = 1 / ε₀.μ₀
c = 299792458m/s (6.70616632E+008 mi/h)
This value was fixed by convention as a result of declaring one meter as the distance traveled by a specific light source# in a vacuum in 1/299792458 seconds (CGPM Oct/1983) and is therefore considered to be exact.
#The radiation used for this convention was from the 'iodine stabilized Helium-Neon laser' (wavelength = 632.99139822nm)

Linear Expansivity (α)

see Coefficient of Expansion

Liquid

A substance in a state whereby attraction due to gravity is greater than attraction between the atoms (or molecules)
and occupies a constant volume but a variable shape

A liquid will always occupy the lowest possible space in a container

This state occurs between the gas and solid states for all substances

Locus

The path generated by a point following a mathematical equation.

for example: the locus of a point 'x,y' following the equation:
r² = (x - a) + (y - b)²
will draw a circle of radius 'r' centred at position 'a,b'

Logarithm
(log, log₁₀)

The logarithm value of a number
The logarithmic base may be any positive number but is usually 10

see Logs and Trig-technical help
see also Natural Logarithm

Longitude (Lon)

The vertical (pole to pole) grid-lines that divide the surface of the earth into 360 equal spherical wedges (1°)
0° & 360° gridlines run through the Royal Observatory at Greenwich, England (see internet for John Harrison)

The horizontal distance between each gridline at the equator = 111319.8922m
The horizontal distance between each gridline at the poles = 0m
The surface area between two gridlines = 1.41548E+12m²

Longitudinal Stress

Primary stress parallel with the axis of a component

Magnetic Constant
(μ₀)

The permeability of free space (a vacuum)
μ₀ = 4.π / 1E+07 H/m
also called vacuum permeability

This value was fixed by convention and is therefore considered to be exact.

Magnetism

The attraction between metals due to electron spin and alignment

Some magnetic materials are listed below:
Iron: The most common magnetic material
Neodymium: The strongest of all permanent magnets
Cobalt: Highest Curie point
Gadolinium: Curie point at room temperature
Terbium: Changes shape in a magnetic field
Dysprosium: Alloying element for special magnets

Magnetic Quantum Number (m)

The third in a set of quantum numbers that describes the energy level of the electron

The magnetic quantum number of an electron can be a positive or negative integer: i.e. -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, etc.

The magnetic quantum number must be different for each electron in the same shell with the same azimuthal and spin quantum numbers

Marageing

An ageing heat treatment procedure used to harden, strengthen & toughen certain alloys (most alloys do not respond to this process).

The age hardening process is performed as follows:
The alloy is quenched from a suitable temperature (e.g. 500°C for Duralumin) and then left at room temperature for about a week.
This process can be accelerated in some alloys by increasing the storage temperature from ambient to about 180°C

A marageing alloy can therefore be machined or formed easily and subsequently strengthened with age over a very short period.

The word originates from 'mar' for martensite (the steel structure) and 'ageing' to describe the process
It is frequently spelt 'maraging' by misspelling 'ageing' as 'aging'

see Stainless Steels

Martensite

Super saturated austenite created by rapid cooling (quenching). Carbon exists in sharp clumps between the grains of iron making it hard and brittle. Tempering after quenching allows the excess carbon to form smaller spheroids and redistribute itself reducing hardness and brittleness

Mass

The quantity of matter in a body equivalent to its inertia and is measured in kg, lbs, etc.

The mass of a body is equal to:
a) its weight divided by the coincident gravitational acceleration
and
b) its density multiplied by its volume

This property for any given body remains the same irrespective of liquifaction, dissection and location (in the iniverse)

Maximum Metal Condition
(MMC+)

The condition of at least two assembled components that when machined within required dimensional tolerances results in the removal of the least material

Whilst convention does not differentiate between minimum and maximum metal conditions when using the symbol 'MMC', CalQlata always uses MMC+ for this condition

see Symbols

Mechanical Equivalent of Heat (J)

A conversion factor for heat energy and work energy
{4.1868 Joules = 1 calorie}
4.1868 J/g is the specific heat capacity of water @ 100°C

Calculations using metric units;
J = 1.0

Calculations using Imperial units;
J = 4.1868 J/cal = 778.16937097 ft.lbf/Btu

Median

A straight line that joins a vertex with the centre of the opposite side

Member

A longitudinal component such as a structural element, rod, bar or beam

Membrane

A large plate or sheet of relatively thin wall than can comprise any natural or manufactured material

Membrane Stress

Tensile or bending stress in the flat plane of a membrane

see also Membrane

Meson

A pair of sub-atomic particles comprising one quark and one anti-quark (part of the Hadron particle family)

Mesosphere

The ceiling for 99.95% of nitrogen, the earth's most abundant atmospheric gas (Stratosphere to 80km)

Stratum of the earth's atmosphere that comprises the ceiling of normal atmospheric gases (see Ionosphere)

Temperature reduces with increasing altitude

Metacentre

The metacentre and metacentric height of a vessel

The point at which a vertical line passing through the centre of buoyancy of a slightly tilted vessel meets a line through its centre of gravity (see image).

Metacentric height:
the vertical distance between the centre of gravity of a vessel and its metacentre

The vessel is stable if the metacentre is above the centre of gravity and unstable if it is below.

A vessel's stability is defined by the metacentric height.
The greater the height the more stable the vessel.

Metallic Bonds

Metallic elements lose electrons freely generating a cloud or sea of electrons in which positively charged metal atoms (cations) are held together.

Metallic bonds tend to be the easiest to form and also the easiest to break, making metals the most versatile of the elements.

see also Covalent and Ionic bonds

Microwaves

Long wave electromagnetic radiation that falls between infra-red light and radio-waves

Ranges from:
0.001m < λ < 0.1m
(2.99792459E+11Hz > ʄ > 2.99792459E+09Hz)

Minimum Metal Condition
(MMC-)

The condition of at least two assembled components that when machined within required dimensional tolerances results in the removal of the most material

Whilst convention does not differentiate between minimum and maximum metal conditions when using the symbol 'MMC', CalQlata always uses MMC- for this condition
see Symbols

Mode

mode

The beam length deflected between two nodes

see also Amplitude

Molarity

The number of moles of an ion per litre of solution

Mole

The mass of a material that contains Avogadro's number (6.0221415E+023) of units (e.g. atoms, molecules, etc.)

For example;
One mole of carbon (12.01 RAM) contains 6.02214129E+023 atoms and weighs 12.01g
One mole of a substance, also containing 6.02214129E+023 atoms, with three times the relative atomic mass of carbon '36.03 RAM' (3 x 12.01) will therefore weigh 3 times as much as carbon, i.e. 36.03g

Molecular Density

The mass density (g/m³) of a substance divided by its relative atomic mass (g/mole)

ρᴹ = ρ ÷ RAM (moles/m³)

see also Molecular Weight

Molecular Weight

The sum of relative atomic masses comprising a molecule
For example:
The molecular weight of water (H₂O):
2 x 1.00794 + 1 x 15.9994 = 18.01528 (dimensionless)

This calculation can also be applied to a mixure of gases (i.e. not a molecule) in order to specify its molecular weight
For example:
The molecular weight of air (excluding trace elements):
N₂ (78.087%) RAM: 28.0134 = 0.78087 x 28.0134
O₂ (20.95%) RAM: 31.9988 = 0.2095 x 31.9988
Ar (0.93%) RAM: 39.948 = 0.0093 x 39.948
CO₂ (0.03%) RAM: 44.0095 = 0.0003 x 44.0095
RAMₐᵢᵣ ≈ 21.875 + 6.704 + 0.3715 + 0.0132 ≈ 28.9633
Note: including all trace elements RAMₐᵢᵣ = 29.32406451

Molecule

The smallest part of a substance that still exhibits the chemical properties of the substance

A molecule is at least two electrically charged ions joined together by sharing electrons/valences/energy in order to reduce their collective electrical charge

Moment (M)

An applied load or centre of area a given distance from a datum

Also known as torque or rotational moment or bending moment or area moment

Moment Couple

Moment Couple

Two parallel opposing forces applied a specified distance from each other

Moment of Inertia (I)
(of an area)

Also (incorrectly) known as second moment of area, describes the mass of a body about its neutral axis

That is, the sum of all the particle masses multiplied by the square of their distances from the neutral axis (radii of gyration)

I = A.ɍ²

Moment of Inertia (I̊)
(rotational)

Inertia possessed by a body rotating about a central axis

I̊ = m.ɍ²

Momentum (p)

A quantity of straight-line motion of a body equal to its mass multiplied by its velocity;
p = m.v (kg.m/s)

Also a measure of force (m.a) multiplied by its period of application (in seconds);
p = t.m.a (s.kg.m/s² = kg.m/s)

Monoclinic

The arrangement of atoms within the shape of a single metal crystal.

This crystal shape is a single atom located as close as possible to its neighbour.

Morse Taper

A conical shaft and mating sleeve for machine-part self-holding applications that optimises assembly load, holding capacity and easy release (without damage). The tapered shaft is normally driven by an End-Tang (or Key) or a Longitudinal Key.

Different size numbers (0 to 7) relate to different engaged lengths (1-15/16" to 9-1/2")

Morse's nominal included angle is 2.86419236832929°
However, as each size is based upon standard fractional lengths and diameters, not all tapers (0.05 and 0.052 inches per inch) will have exactly the same angle (2.86° to 3.0°)

The optimum angle for a coefficient of friction of 0.8 for clean, dry, ground, carbon steel surfaces is 2.9745503204919°

The Morse Taper is a direct alternative to the Jarno Taper and used for similar applications to the Brown & Sharpe Taper

Most Damaging Stress-Block

The stress-block that lies closest to the S-N curve, within a group of stress-blocks that together constitute the fatigue life of a material or mechanical component

Motor

A motor is a generator that acts in reverse (see MotAtors).

Copper wire coils are rotated within the field of magnets. A current applied to the wire coils induces relative rotation of the magnets. This rotation of a central shaft or outer body is used to do physical work.

Muon

An elementary particle similar to the electron (also with a negative electric charge) but much heavier

A muon is classified as a lepton

m=1.884273466E-25g [105.7MeV/c²], lifetime=2.2μs

Natural Frequency (ƒⁿ)

see Frequency

Natural Period

see Frequency

Nappe (conic)

One of two sheets on either side of the vertex forming a cone

Natural Logarithm
(Ln, logₑ)

The logarithm value of a number, the base of which is 2.71828182845905

see Logs & Trig-technical help

see also Logarithm

Necking
(plastic deformation in metals)

The reduction in cross-sectional area of a metal object exposed to a tensile stress greater than UTS but less than breaking stress

Neutral Axis

The plane through a bending body in which no tension or compression occurs

Note: tension occurs in the material on convex side of the neutral axis and compression occurs in the material on concave side

Neutrino

An elementary particle with minuscule but nonzero mass that often travels close to the speed of light, that lacks an electric charge and is able to pass through ordinary matter almost undisturbed and are thus extremely difficult to detect

A neutrino is classified as a lepton

Neutrinos are created as a result of certain types of radioactive decay or nuclear reactions such as those that take place in the Sun, in nuclear reactors, or when cosmic rays hit atoms.

There are three types, or "flavours", of neutrinos: electron neutrinos, muon neutrinos and tauon neutrinos; each type also has an antimatter partner, called an anti-neutrino.
Electron neutrinos or anti-neutrinos are generated whenever neutrons change into protons or vice versa, the two forms of beta decay.

Interactions involving neutrinos are generally mediated by the weak force

Neutron

An electrically neutral particle in the nucleus of an atom that contains 1 up quark and 2 down quarks (along with other elementary particles e.g. bosons, gluons, etc.)

m=1.6749272928E-024g [939.565398MeV/c²],
Rad=1.113284057367E-15m, Lifetime>885.7s (free), Q=0, Iz

Newton's
Laws of Motion

1ˢᵗ Every mass retains its momentum (including rest) until a force acts upon it (Galileo's law of inertia)

2ⁿᵈ A change in momentum is proportional to, and acts in the direction of, the applied force

3ʳᵈ To every action there is an equal and opposite reaction

see Laws of Motion

Nobility
(noble metals)

Describes the chemical stability of a metal.

The more noble a metal (e.g. gold, silver, platinum, etc.) the less chemically active it is.

The least noble metals, which include caesium, sodium and magnesium are all highly reactive.

A noble metal is electrically positive; i.e. it has a high affinity for electrons (see electronegativity). As a rule, the higher the electronegativity of a metal, the more noble it is. Therefore, whilst electronegativity cannot be used as a measure of nobility it may be used as a guide.

see Galvanic Corrosion

Nodal Points
(of a lens)

Nodal points of an optical lens

Two points on the axis of a Lens such that an entering ray of light would theoretically project through to one nodal point (ignoring refraction) and appear to exit the lens from the other nodal point, parallel to the entering ray.

The angle at which a such a light-ray must enter the lens varies with its radial distance from the lens axis and only occurs at radii close to it.

The primary nodal point refers to the point at the front of the lens
The secondary nodal point refers to the point at the back of the lens

As the radial distance (from the lens axis) of the entering light-ray tends towards zero, the nodal point (primary or secondary) of a lens will coincide with the associated principal point if the refractive index of the environments are identical both sides of the lens.

Node

node

The points of intersection at each end of a mode

Normal
(angular)

'Normal to' is an expression used to describe the relationship of one direction being at right angles to another

Normalise
(carbon steel)

To normalise a steel alloy is to optimise its strength by heat treatment without making the material hard (brittle).

Carbon steel is normalised by heating it above 723°C, holding it there to allow all the material to transform to austenite and allowing it to cool naturally in still air, i.e. more quickly than annealing.

Oblique (triangle)

A triangle in which none of the angles equal 90°

Oblong

A three-dimensional, six-sided figure, each side of which is 90° to its adjacent sides

see also Rectangle

Obtuse (angle)

An angle between 90° and 180°

Open Hearth

The Open Hearth is a process for making steel (it is also called the Siemens-Martin process).

It directs the waste heat given off by the furnace through an open firebrick lining, heating the brick-work to a very high temperature. The same pathway is also used for introducing preheated air into the furnace significantly increasing the melt temperature.

This process is gradually replacing the Bessemer Converter.

Orbit

A curved (e.g. elliptical) path generated by a body travelling around a central point that is maintained by equal and opposite centripetal and centrifugal forces

Fᵖ = m.g = ½.m.v² / r
i.e. g = v² / 2.r and r = v² / 2.g
where 'r' is the natural orbital radius of any given orbiting mass travelling around a central mass at a given velocity

Order
(thermodynamics)

see Disorder

Overpressure

A pressure higher than ambient

It is normally measured in multiples of unit ambient pressure such as bar or atmospheres, e.g...
10 tam (or 10 bar) is 10 times as high as ambient pressure

Ozone

Oxygen molecules (O₂) are split apart by the sun's ultra-violet light radiation and the two resultant oxygen atoms then bond to other oxygen molecules to produce ozone (O₃).

Ozone is unstable and converts back to oxygen molecules as it falls into the troposphere where it reacts with other gases.

see Ozone Layer for an explanation of the 'hole'.

Pappus theorum

The calculation of volumes by rotating an area about a central axis

E.g. V = 2πRA
where;
V is the volume of the swept area
A is the rotating area
R is the radius from the centre of gravity of final volume to the centre of area (A)

Parabola

Conic Parabola

The perimeter of any plane cut through a right-circular cone parallel to its slope

where; y² = 2.p.x
eccentricity = 1

see Elliptical Curves
see also Conic

Parallelepiped

Any three-dimensional figure with six faces, four of which are dimensionally equal and parallel and the two ends are also parallel and dimensionally equal.

Also described as a three dimensional rectangle of constant thickness.

A special Parallelepiped is a cube where all 6 faces are dimensionally equal.

Parallel Lay
(wire rope)

All strands are wrapped parallel to each other, i.e. in the same helical direction

Paramagnetism

The attraction of a non-magnetic material towards a magnet
(magnetic attraction tends to be weak)

Paraxial
(lens)

A ray of light travelling towards the front face of a lens very close to its axis and parallel to it.

Partial Pressure

The pressure of each gas occupying a space or container in a mixture of fluids

see Partial Pressure-technical help
see also Dalton's Law

Particle

The smallest constituent part (atom or molecule) of a substance that possesses the same properties as the substance in bulk

Pauli's Exclusion Principle

Only one fermion can occupy a quantum state at a given time
Therefore if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest

Pearlite

Alternate layers of cementite and ferrite generated as austenite containing 0.83% carbon cools below 723°C

Pearlite contains the same amount of carbon as the maximum carbon carrying capacity austenite (0.83%)

Perigee

the perigee of an orbiting planet

The nearest point an orbiting body gets to its attracting mass

Whilst this term can also be used instead of Perihelion (i.e. it means the same thing), it is normally used to describe the point at which the distance between earth and its orbiting moon is smallest
This term is made up of the Greek prefix peri for 'around' or 'about', and the Greek word gee for the earth.

a = half the width of the elipse
e = its eccentricity

see also Aphelion and Apogee

Perihelion

the perihelion of an orbiting planet

The nearest point an orbiting body gets to its attracting mass

Whilst this term can also be used instead of Perigee (i.e. it means the same thing), it is normally used to describe the point at which the distance between sun and its orbiting planet is smallest
This term is made up of the Greek prefix peri for 'around' or 'about', and helion from 'Helios' the Greek sun god.

a = half the width of the elipse
e = its eccentricity

see also Aphelion and Apogee

Permeability
(μ)

The ratio of magnetic flux density in a medium to the magnetising force producing it.

The permeability of free space (i.e. in a vacuum) is the Magnetic Constant

Permittivity
(ε)

The ratio of electric displacement in a medium to electric field intensity producing it.
also called dialectric constant or specific inductive capacity

The permittivity of free space (i.e. a vacuum):
ε₀ = 1 / μ₀.c² = 8.8541878176204E-12 Farad per meter

Because the speed of light in a vacuum and the magnetic constant are both considered to be exact values, this too is considered to be an exact value.

Perpendicular

At 'a right angle' or '90°' or 'normal' to a line or surface

Phase Angle (electrical)

alternating current

The angle of shift between the alternating current and the voltage in an AC power supply.

As the current in an inductive AC power supply will peak after the voltage, it is said that the current 'lags' the voltage.

As the current in a capacitive AC power supply will peak before the voltage, it is said that the current 'leads' the voltage.

If there is only inductive or capacitive resistance in an AC power supply, i.e. there is zero resistance in the conductor, the phase angle will be 90°.

If there is no inductive or capacitive resistance in an AC power supply the phase angle will be 0°.

Electrical resistance in the conductor will shift the phase angle between 0° and 90°. The Arccosine of this 'Phase Angle' is the Power Factor of the supply.

see also Apparent Power and True Power

Phase Diagram

An equibrium diagram of an alloy metal that defines the natural crystal structure of specific alloy compositions at specific temperatures.
Also called an equilibrium diagram.

see Copper Alloys, Metal Properties and Carbon Steels

Photon

An elementary particle that emits electromagnetic radiation (light) equal to Planck's constant multiplied by its frequency
In this case;
frequency = speed of light (c) ÷ wavelength of the photon (λ)

A photon is a Gauge Boson

m=0g, Ø≈0m, lifetime<10¹⁸yrs, Q=0, Iz=1

pi (π)

The ratio between a circle's circumference and its diameter

π is an infinitely long number that can be calculated from the series formula: π² = 6/1² + 6/2² + 6/3² + 6/4² + .....
However, you would need to include a lot of terms to obtain an accurate value for π using this method as the inclusion of even 100,000 terms only reaches a value of 3.14158310432644

CalQlata uses the value of 3.14159265358979 in all its calculators.

Pinned Support

A simple support on a beam

Pipe

An enlosed cylinder of any diameter or length

Thin-wall pipe (general): t < R÷10

Pitch (vessels)

Pitch

The rotational movement of a vessel about the lateral ('y') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Planck's Constant (h)

Planck's law states that the energy of an electromagnetic wave is confined to indivisible packets (quanta) each of which has to be radiated or absorbed as a whole and the magnitude of this energy is proproportional to its frequency.

If E is the energy (J) and ƒ is the frequency of the electromagnetic radiation (/s) then:
h = E/ƒ = E.λ / c = E / Rᵧ.c = √(π.mₑ.e².aₒ / ε₀)
   = 6.62607174469163E-34 J.s
where:
Rᵧ = Rydberg's constant
c = speed of light in a vacuum
mₑ = electron rest mass
e = elementary charge unit
aₒ = Bohr radius
ε₀ = permittivity of free space

Planck's values are calculated below:
Planck's time; t = (ħ.G / c⁵)⁰˙⁵ = 5.39133511680329E-44 s
Planck's length; ℓ = (ħ.G / c³)⁰˙⁵ = 1.61628161195951E-35 m
Planck's mass; m = (ħ.c / G)⁰˙⁵ = 2.17639905730512E-08 kg
where:
ħ = Dirac's constant
G = Gravitational constant
c = speed of light in a vacuum

Plastic Strain

A material that does not return to its pre-deformation dimensions when stress is released
(i.e. does not obey Hooke's Law)

Plow Steel

A high quality, high strength carbon steel (0.5% to 0.95%) used to manufacture 'Bead Wire'

Point Load

An applied force that is concentrated at a single point

Poisson's Ratio (v)

The relationship between axial stress and the lateral deformation when applied to a body that obeys Hooke's Law;
where v = (E / 2.G) – 1

Poisson's ratio varies in magnitude between 0 for a totally brittle body (no deformation whatsoever) and 0.5 for a perfect elastomer (same deformation in all three directions). 0.3 is normally used for carbon steel

Polar
Co-Ordinates

Polar Co-Ordinates

The directional definition of a vector using its angular relationship to 2-D (α,r) or 3-D (α,β,r) axes

see also Cartesian Co-Ordinates and Vector

Polar Moment of Inertia (J)

Describes the structural strength of a cross-sectional area, or a numerical representation of its resistance to torsional deformation
It also describes the rotational moment of inertia of a solid shape {kg.m² or lb.ft²}, e.g. of a cylinder or sphere

The polar moment of inertia of any shape is the sum of any two second moments of area (of the same shape) at 90° to each other
Note: The sum of any two moments of inertia at 90° to each other of any shape will always be equal to the sum of any other two moments of inertia at 90° to each other for the same shape and about the same centre of rotation, irrespective of their relative orientation

Polygon

A 2-D shape with three or more sides

A Regular polygon has equal sides and an irregular polygon has unequal sides

Polytropic
(thermodynamics)

A process in which the relationship between pressure, volume and ratio of specific heats of an ideal gas in a system remain constant and can be defined thus: p.Vn = K

Where:
p is the pressure of an ideal gas
V is the volume of the system
K remains constant for all stages of the process
n varies with the type of process, e.g.:
   Isothermal; n = 1
   Isentropic; n = γ (specific heat ratio)
   constant pressure; n = 0
   constant volume; n = ∞

see Thermodynamics
see also Adiabatic, Isochoric and Isobaric

Positron

A positive electron of the same mass and electrical charge (but opposite sign) as an electron

Positrons are produced in the decay of radio-isotopes and X-rays of energy greater than 1MeV

Potential-Difference (PD)

The electrical difference between two discrete points generated by an electro-motive force

The unit of measurement is a Volt which equals one Joule of work done by one coulomb moving between them

Potential Energy (Uᴾ)

The energy stored in a system or body

It could be stored in a compressed (or stretched) spring:
Uᴾ = ½ky² ÷ gc
or
It could be stored in a body raised above the ground:
Uᴾ = mgh ÷ gc

Where:
k = spring constant (see Hooke's Law)
y = deformation of spring
m = mass of body
g = gravitational acceleration
h = distance from point of impact (e.g. height above ground)
gc = Gravitational Constant (dimensionless)

Potential-Hydrogen
(pH)

Potential Hydrogen (sometimes referred to as the 'power of hydrogen') defines the positive hydrogen ion activity in a solution
Low hydrogen activity means the +ve Hydrogen ion (H+) molarity of a solution is less than 10⁻⁷ and is said to be acidic (pH<7)
The +ve Hydrogen ion molarity of a neutral solution (e.g. pure water) is 10⁻⁷ (pH=7)
High hydrogen activity means the +ve Hydrogen ion (H+) molarity of a solution is more than 10⁻⁷ and is said to be alkaline (pH>7)

pH can be calculated using the following formula:
pH = -Log₁₀(aH+) or Log₁₀(1/aH+); where aH+ is the +ve hydrogen ion molarity of the solution (i.e. the number of moles of H+ ions in one litre of the solution; 'a' represents the atomic element(s) attached to the H+ e.g. OH₃ is an aH+ ion)

Power

Work carried out over a given period of time or the rate of doing work

The faster work is done, the more power is expended

The units of measurement are; Btu/h, W, J/s, cal/min, N.m/s, lbf.ft/min etc.

Power
(of a lens)

The reciprocal of the focal length (ƒ) of a lens
P = 1/ƒ

Power Factor (electrical)

The factor applied to the Apparent Power of an alternating circuit in order to convert it into True Power

It is calculated thus: p.f. = Resistance ÷ Impedance and is the cosine of the Phase Angle between the alternating current and the alternating voltage.

Pressure Vessel

An enclosure of any shape that will contain or resist a fluid under pressure without leakage

Thin-wall vessel: t < Ø÷10

Pressure Welding

Press two or more metals together with sufficient presssure to cause metal fusion between them.
This process may be carried out at an elevated temperature to assist the welding process.

Primary Stress

The three uni-directional tensile stresses oriented along the 3-D axes (see Right-Hand Rule) of a mechanical component

Principal Planes
(of a lens)

Principal planes of an optical lens

The curved planes that trace the principal points of light-rays entering a lens parallel to its axis.

The primary principal plane refers to the plane at the front of the lens
The secondary principal plane refers to the plane at the back of the lens

Principal Points
(of a lens)

Principal points of an optical lens

The theoretical points of intersection of light-ray projections after entering and before exiting a lens.

The primary principal points refers to those at the front of the lens
The secondary principal points refers to those at the back of the lens

see also Principal Planes and Nodal Points

Principal Quantum Number (n)

The first in a set of numbers that uniquely describes the quantum state of an electron

The principal quantum number of an electron can only be a positive integer and identifies the shell number it occupies:
i.e. 1, 2, 3, 4, 5, 6, 7, etc.

All other electrons in the same shell will have the same principal quantum number but at least one of its other quantum numbers must be different

Principal Stress

A primary stress reoriented (in space) and altered in magnitude as a result of simultaneous shear stresses

Prism

A longitudinal body with sides of equal width and constant cross-section. The term for a prism usually ends with '....hedron'.

For example:
Trihedron (3 sides)
Quadrahedron (4 sides)
Pentahedron (5 sides)
Hexahedron (6 sides)
Heptahedron (7 sides)
Octahedron (8 sides)
Nonahedron (9 sides)
Decahedron (10 sides)
Hendahedron (11 sides)
Dodecahedron (12 sides)
etc.
Cylinder (∞ sides)

Process
(thermodynamics)

Any alteration in the energy of a system

Any change in the physical properties of a system will require a change in its energy, either by addition or removal
and the physical properties of a system include: temperature; pressure; volume; dimensions; state (gas-liquid-solid); force; movement; etc.

Reversible Process:
One in which both the system and its surroundings can be returned to their original states with or without the addition of more energy.
There will be no loss in the ability of a system to do work if the process is reversible.

Irreversible Process:
One in which neither the system nor its surroundings can be returned to its original state with or without the addition of more energy.
There will be a loss in the ability of a system to do work if the process is irreversible.

Prograde
(rotation)

The same direction of rotation as the spin (rotation) of a force centre

For example, the sun in our solar system spins in a clockwise direction looking down on top of it
All the planets orbitting and/or spinning in a clockwise direction are said to orbit and/or rotate in a prograde direction

see also Sidereal and Retrograde

Proton

A positively charged particle in the nucleus of an atom that contains 2 up quarks and 1 down quarks (along with other elementary particles e.g. Bosons, Gluons, etc.)

m=1.67262163783E-024g [938.27202MeV/c²],
Rad=1.112772961016E-15m, Lifetime>2.1E+29 years, Q=1e, Iz

Pyramid

A regular or irregular three-dimensional prism or cone with a pointed cap

see also Frustum

Quadrangle

An irregularly shaped four sided figure
(see Quadrilateral)

Quadrilateral

A regularly shaped four sided figure

CalQlata consider all quadrilaterals to be four-sided figures with all internal angles equal to 90°
(see Quadrangle)

Quantum Number

One of a set of numbers that uniquely describe the quantum state of an electron
The numbers are integers or half integers and positive or negative
The numbers include; principal (n), azimuthal (ℓ), magnetic (m) and spin (s)

Quark

The family of sub-atomic particles within the fermion group that constitute the constituents of matter

Quarks combine to form composite particles called hadrons, the most well-known of which are protons and neutrons

There are 6 quarks:
up, down, charm, strange, top & bottom

Quench

The rapid cooling of a heated steel alloy to lock in an unnatural crystal structure to harden and strengthen it.

Cooling may be carried out by liquids, solids or gases.

Radial

At right-angles to a central axis

Radial Stress

Primary stress at right-angles to (out-of-plane with) both longitudinal and lateral (or hoop) stresses

Radian

An angle expressed in terms of π

π radians = 180°
any angle 'A°' expressed in radians = A x π ÷ 180

Radiation

The emittance of energy from a source, the intensity of which declines at the square of the distance from the source in the absence of an absorption resource.

Radioactivity

The product of changing one isotope into another isotope
i.e. when atoms lose or gain neutrons (alpha & beta particles)
or
the emission of electro magnetic energy (gamma)

Radio Waves

Very long-wave electromagnetic radiation used for the transmission of sound

λ > 0.1m (ʄ < 2.99792459E+08Hz)

Radius of Gyration (ɍ)

The distance from an axis of rotation to the centre of area (or mass)

ɍ = √(I/A) and ɍ = √(I/m)
where:
I = second moment of area
A = area of section
m = mass

Ratio of Specific Heats
(γ)

γ = cp ÷ cv

monatomic gases (i.e. gases comprising one element): γ ≈ 1.67

diatomic gases (i.e. gases comprising two elements): γ ≈ 1.4

polyatomic gases (i.e. gases comprising more than two elements): 1.0 < γ < 1.4

see also Specific Heat(s)

Reactance (electrical)

Reactance ('X') of inductance ('L') or capacitance ('C') is their resistance equivalent in an AC current.

where:
X = 2.π.ƒ.L (inductance)
and
X = 1/(2.π.ƒ.C) (conductance)

ƒ = frequency

Recrystallisation

The movement of atoms in a metal lattice structure towards a low energy position.

After cold working or heat treatment, a residual stress is generated in a metal by atoms having been forced away from their natural position within the lattice structure.
Annealing allows these atoms to move back to their natural position in the lattice structure relieving internal stresses.

Rectangle

A two-dimensional, four-sided figure, each side of which is 90° to its adjacent sides

see also Oblong

Refractive Index

The ratio of the phase velocity of electromagnetic radiation in a vacuum and its phase velocity in a medium

For example:
the phase velocity of light in air is 1.00292 slower than in a vacuum so the refractive index of air is 1.00292
and
the phase velocity of light in water is 1.3333 slower than in a vacuum so the refractive index of water is 1.3333

see also Snell's Law

Refraction

The bending of light (or any electromagnetic wave) by altering its velocity; e,g, as it passes between media of different densities.

see also Refractive Index

Regular Lay

A particular type of helical lay pattern in a wire rope where the filaments are wrapped within each strand in the opposite helical direction as the strands are wrapped within the wire rope. In a manufactured wire rope, the filaments run parallel with the long axis of the wire rope (see image).

Regular Lay

You can have 'right lay' or 'left lay' configurations:
In a 'right lay' configuration the strands follow the same helical direction as a right-hand screw thread
(see image)
In a 'left lay' configuration the strands follow the same helical direction as a left-hand screw thread
(opposite to image)

Whilst these wire ropes provide less wear resistance than 'Lang lay' constructions due to their undulating (peaky) surface and lower bending fatigue resistance, the structure is much more stable and resistant to abuse.

Regular lay wire ropes are generally used for all non-specialist applications.

see also Lang Lay

Relative Atomic Mass
(RAM)

The mass number of the most stable isotope of an element
the RAM of an element is also its specific mass in grams per mole (g/mol)

For example, if Iron (Fe), which has an atomic number of 26, had the same number of protons and neutrons, its RAM would be 52 yet its actual value is 55.847. This means that in its most stable condition Iron's atoms contain more neutrons that protons and that this excess varies in any bulk of its material.

'Elements' calculates RAM values for all molecules

Resistance (R)

The static resistance (the unit of measurement is the Ohm) in a conductor due to its material resistivity, its cross-sectional area, its length and its temperature.

The pipeline analogy for resistance is an internal restriction such as a helical vane or venturi both of which restrict flow but provide work and generates the pressure drop across the inlet and outlet of the pipe.

R = V.I
where: I = current and V = voltage

Resistor

A material that prevents movement of its electrons when exposed to a potential difference

This term is relative (see Conductor). You can have a good resistor and a bad resistor. The better the resistor, the harder it is for its electrons to flow

Resonance
(vibration)

A vibration that occurs in a sprung system at or close to its natural frequency during which deflections are amplified

Response Amplitude (RA)
(vessels)

The amount of movement in a vessel at sea (linear and rotary) generated by a passing hydrodynamic wave in six degrees of freedom
Linear movement is measured in units of length (m, ft, etc.) &
rotary movement is measured in angular units (° or rads)

see also Heave, Surge, Sway, Pitch, Roll and Yaw

Response Amplitude Operator (RAO)
(vessels)

A factor that must be multiplied by a wave height or slope (wave or water) in order to define a resposnse amplitude
Linear movement is measured in lengths per unit length
(m/m, ft/ft, etc.) &
rotary movement is measured angles per unit length or angle
(°/m, °/°, rads/rad,etc.)

Also called a 'transfer function', which refers to the transfer of motion in a specified wave to the motion of the body (e.g. ship)

Rest Mass

The mass of a body immediately prior to annihilation at light-speed as originally defined by Henri Poincaré

Retrograde
(rotation)

The opposte direction of rotation as the spin (rotation) of a force centre

For example, the sun in our solar system spins in a clockwise direction looking down on top of it
All the planets orbitting and/or spinning in an anti-clockwise direction are said to orbit and/or rotate in a retrograde direction

see also Sidereal and Prograde

Rhombic

rhombic

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain eight closely packed atoms, each of which are located at each corner of a cube that has slipped to form a rhomboid prism.

Right-Angle

An angle of exactly 90°

Right-Hand Rule

Linear Right Hand Rule

The thumb, index and middle fingers of the right hand are projected at 90° to each other in three dimensions, where the index finger represents the x-axis (Surge), the middle finger represents the y-axis (Sway) and the thumb represents the z-axis (Heave)

Rotary Right Hand Rule

This definition also refers to the direction of rotational twist about the vector axes; the thumb of the right hand is projected in the direction of the axes defined above and the four fingers naturally curled in towards the palm of the hand. The positive direction of rotation {xy(Yaw), xz(Pitch), yz(Roll} are in the direction of the four fingers

Right-Angle Triangle

A triangle with one of its angles at exactly 90°

Roentgen [Röntgen]
(R)

The unit of radiation exposure, dedicated to the discoverer of x-rays (Wilhelm C Röntgen).
The exposure to 1 Roentgen is equal to the absorption of
0.00838 J/kg

Also described as the charge per unit mass (of air), equal to 2.58E-04 C/kg, generated by ionisation from x or γ-radiation

Roll (vessels)

Roll

The rotational movement of a vessel about the longitudinal ('x') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Rydberg Formula
& Constants

Johannes Rydberg developed his formula to calculate the wavelength of a photon that would be emitted when an electron drops from a high initial energy state (shell nᵒ: n₁) to a low final energy state (shell nᵒ: n₂), which can be calculated thus:
λ = 1 / R.Z²(1/n₁² - 1/n₂²)

Rydberg's universal constants for the limiting conditions are provided below:

Minimum wavelength (maximum wave number):
R = mₑ.e⁴ / 8.ε₀².h³.c = 1.09737269561359E+07 /m

Electron energy at ground state:
Rᵧ = R.h.c.(Z/n)² = 2.17987197684936E-18 J
which can be converted to eV thus:
Rᵧ = Rᵧ/e = 13.605691968492 eV

Where:
R = Rydberg constant (above)
mₑ = electron mass
mp = mass of protons in nucleus
e = elementary charge unit
ε₀ = permittivity of free-space
h = planck's constant
c = speed of light in a vacuum
Z = atomic number
n = electron number (1, 2, 3, etc.)

Nils Bohr developed alternative values for R and Rᵧ based upon
reduced mass; mₑ/(1 + mₑ/mp):
R = R / (1+mₑ/mp) = 1.0967753777734E+07 /m
R = Rᵧ / (1+mₑ/mp) = 2.1786854190384E-18 J

Safety Factor

The proportion of additional stress (or use) that can be applied to a material (or component) before it fails.

For example: if you design a component to experience less than or equal to 200 N/m² of stress and the material from which it has been manufactured has a minimum specified yield stress of 400 N/m², the component has a safety factor of 2

Safety factor is the inverse of utilisation

Satellite

A mass orbiting a force centre under the influence of gravitational force.

For example:
The earth is a satellite of the sun
Our Moon is a satellite of the earth

Saturation
(fluids)

The ability of a fluid to hold another substance (gas, liquid or solid) in suspension that varies with pressure and temperature

High temperatures low pressures raise the saturation level

Scalar
(quantity)

A quantity (magnitude) that has no direction, such as;
volume, density, area, etc.

see also Vector

Schwartzschild
radius (R)

Karl Schwartzschild's formula to determine the radius of a mass that would prevent the escape of photons from its surface:
R = 2.G.m/c²
where:
G = Newton's Gravitational constant
m = mass of the star
c = speed of light

Schwartzschild derived his formula from Newton's formula for escape velocity: v² = 2.G.m/R

Seafastening

Welds, padeyes, lugs and other deck attachment facilities used to fix a mass to any part of a ship or vessel in order to prevent unwanted movement whilst in transit at sea

Seastate

The properties of a sequence of following waves defining representative conditions used for equipment design and/or operational conditions.

Seastates are usually compiled from actual data collected from anchored 'buoys' installed in various regions around the world and subsequently sorted seasonally, monthly or daily.

Representative seastates are used for operational, design (e.g. fatigue calculations), extreme, etc. wave sequences for specified weather windows.

Second Moment of Area (I)

Describes the structural strength of a cross-sectional area, or a numerical representation of its resistance to bending deformation

see also Moment of Inertia and Polar Moment of Inertia

Section Modulus (Z)

Describes the ratio of the second moment of area to the distance from the neutral axis of the stressed plane (I/y)

Sector

sector of a circle

A shape enclosed by two radii and an arc of the same circle

Segment

segment of a circle

A shape enclosed by a chord and an arc of the same circle

Self-Holding

When referring to Tapers (Morse, Jarno, Brown & Sharpe, etc.), "Self-holding" describes a condition whereby the assembly (insertion) force is the same as the disassembly (extraction) force and the coefficient of friction between tapered shaft and mating sleeve materials holds them together during use.

Shear Force

Equal and opposite forces induced in a material or substance immediately adjacent to each other, the physical manifestation of which is to cut or tear the material, e.g. as in a pair of scissors.

Shear Modulus (G)

Also known as modulus of Rigidity, is the relationship between shear stress and angular deformation for materials that obey Hooke's law

Shear Stress

Stress induced in a material or substance due to a shear force

Sidreal
(rotation)

The actual rotation of a body, e.g. a planet, with respect to a fixed point in space

This is not the same as the rotation of an orbiting body with respect to its force centre
A planet rotating in the same direction as its orbit will have a shorter rotation [period] with respect to its sun than its sidereal rotation [period]
A planet rotating in the oposite direction as its orbit will have a longer rotation [period] with respect to its sun than its sidereal rotation [period]

see also Prograde and Retrograde

Simple Support

A support that prevents only one degree of freedom, which is at right-angles to the load

Simpson's Rule

An algebraic solution for integrals that are dificult or impossible to solve by integration

see Integration Methods

Sinter

The coalescing (conglomeration) of solid particles using heat but without actually melting (liquifying) the material.

Sinusoidal

A continuous curve with the same x,y relationship as the Sine of an angle

Slag

The unwanted (remnant) material left over after extracting a material from an ore.

Slag contains commercially valueless material and an amalgamation flux.

Slugging

The thickening or solidification of a heavy liquid in a pipe or constricted passage that prevents free-flow conditions.

Smelt

The extraction of a metal from an ore by melting.

During melting, the ore will seperate into two layers: a lower layer of molten metal and an upper layer of slag.

S-N Curve

The graphical representation (normally a straight-line Log10-Log10 plot) of maximum allowable stress range plotted against the maximum possible number of cycles (for this stress range), above which, damage to the material or mechanical component is expected

(S-N = stress number, i.e. the number of stress cycles)

Snell's Law

Snell's law of refraction

Willebrord Snellius: Dutch Proffessor of mathematics at the University of Leiden

Snell's law (1621) states that after passing from one medium of refractive index 'n₁' into a medium of refractive index 'n₂' a ray of light will refract according to the following relationship:
n₁.Sin(θ₁) = n₂.Sin(θ₂)

Solid

A substance in a state where attraction between all of its atoms (or molecules) is greater than gravitational attraction
and occupies a constant volume and with a constant shape

This state occurs at low relative temperatures for all substances

Solubility

The ability of one substance (the solute) to dissolve onto another substance (the solvent)

This ability may be measured in terms of moles per cube (e.g. moles/cm³)

Spar

A principal structural member of an aircraft wing or aerofoil

Special Relativity

Newtonial physics ...
that applies to the laws of gravity and motion of objects moving close to the speed of light
and includes the effects of time

see also General Relativity

Specific Enthalpy (h)
(thermodynamics)

The enthalpy per unit mass of a system

h = u + Rₐ.Ṯ
where;
u = specific internal energy
Rₐ = gas constant
Ṯ = temperature (absolute)

The units of measurement are J/g, Btu/lb, etc.

see Heat Capacity

Specific Entropy (s)
(thermodynamics)

The entropy per unit mass of a system

s = KB.ln(N) = cp.ln(Ṯ) {per molecule}
s = KB.NA.ln(N) = cp.ln(Ṯ) {per mole}
s = KB.NA.ln(N)/RAM = cp.ln(Ṯ)/RAM {per unit mass}
Where;
KB = Boltzmann's constant
NA = Avogadro's number
N = number of microstates
cp = specific heat capacity (constant pressure)
RAM = relative atomic mass
Ṯ = temperature (absolute)

The units of measurement are J/K/mol or J/K/g, Btu/°R/lb-mol or Btu/°R/lb, etc.

see Heat Capacity and Thermodynamics

Specific Gravity (SG)

Also called 'Relative density', is the density of a liquid or a solid relative to pure water (1000 kg/m³). For example, the SG of steel is 7.85 (7850 kg/m³ divided by 1000 kg/m³)

The specific gravity of a gas is quoted relative to the density of air (1.297 kg/m³). For example, the SG of helium is 0.1365 (0.177 kg/m³ ÷ 1.297 kg/m³)

Specific Heat(s)
(cp and cv)

Two specific heat capacities are used in thermodynamic calculations, dependent upon the process (constant pressure or constant volume):

cp is the specific heat capacity of a gas that is heated and allowed to expand whilst maintaining at constant pressure

cv is the specific heat capacity of a gas that is heated in an unchanging volume but where pressure is allowed to vary

see also Heat Capacity and Ratio of Specific Heats

Specific Heat Capacity (cp & cv)

The quantity of heat energy that can be absorbed by a specific substance per unit mass, which varies with temperature

The units of measurement are J/g/K, W.s/g/K, BTu/lb/R, etc.

see also Specific Heat(s) and Heat Capacity

Specific Internal Energy (u)

The internal energy per unit mass of a system

u = Ṯ.cv
where;
Ṯ = temperature (absolute)
cv = specific heat capacity (constant volume)

The units of measurement are J/kg, Btu/lb, etc.

see Thermodynamics
see also Heat Capacity

Specific Volume

Volume per unit mass, or...
the reciprocal of density

Specified Minimum Yield Stress (SMYS)

The minimum yield strength (maximum allowable yield stress) for a material as specified by a recognised authority

Spheroidising
(annealing)

The balling up of the cementite in pearlite during the annealing process
Carbon steel must be held below the lower critical temperature (723°C), ensuring no phase change takes place, allowing sufficient time for the large globules of cementite to break up into small globules and redistribute evenly

Spin Quantum Number (s)

The fourth in a set of quantum numbers that describes the spin direction of the electron

The spin quantum number of an electron can be a positive or negative half integer: i.e. -½ or +½

The spin quantum number must be different for each electron in the same shell with the same azimuthal and magnetic quantum numbers

Spring Coefficient (k)

The proportional relationship between force and movement for an elastic material or a spring
i.e. the amount of force required to deform a material or a spring per unit length

Also referred to as a spring constant and spring rate

Measured in e.g. N/m (lbf/in)

see also Stiffness

Spring Constant (k)

see Spring Coefficient

Sprung System

Any machine or structure, or part thereof, that obeys Hooke's Law, which includes most metals, elastomers (rubber), ceramics, hard-woods, etc.

Spur Gear

A gear wheel, with teeth cut into its circumference at 90° to the plane of the wheel, that normally (but not necessarily) mates with another spur gear

Also referred to as straight-cut gear

The centres of rotation of two mating spur gear wheels are always parallel

Stanchion

A vertical structural member

Steady Flow
(thermodynamics)

A fluid flowing through a system the conditions and properties of which do not change with time.

Stiction

Stiction (static friction) is the resistance to initiate relative movement between two surfaces when forced together

Stiction is always greater than friction

Stiffness

The resistance any material or structure exhibits to deformation

Stiffness can be applied to bending, torsional and axial deformaton and describes the rate of dimensional change for a specified force

see Stiffness & Capacity

see also Spring Coefficient

Strain (e)

The elongation in a material as a result of stress

see also Elastic Strain and Plastic Strain

Strand
(wire rope)

More than one filament wound together

see also Wire Rope

Strange Quark

The third lightest of all the quarks and part of the second generation of matter

The strange quark is classified as a fermion

mᵣ=1.693528659E−25g [95.0MeV/c²], Q=-⅓e, Iz=-½

Stratosphere

The ceiling for 99% of nitrogen, the earth's most abundant atmospheric gas

Altitude @ equator: 15km to 60km
Altitude @ poles: 10km to 50km

Stratum of the earth's atmosphere that comprises mainly nitrogen and oxygen and is considered to be the upper limit of the atmosphere that contains anything of substance

Temperature increases with increasing altitude

Stress (σ, s)

Force per unit area in a material
(similar condition to pressure and defined using the same units; e.g. N/mm² or lbf/in²)

Tensile stress: induced in a material as a result of a positive axial load
Compressive stress: induced in a material as a result of a negative axial load
Shear stress: induced in a material as a result of a shearing (or tearing) action or induced as a result of more than one primary stress
Bending stress: induced in a material as a result of bending - tensile stress at the outside of the bend, compressive stress at the inside of the bend, zero stress at the neutral axis

Failure in materials due to elastic stress is predicted using various theories: Principal stress (Rankine), Principal strain (e.g. St Venant) or strain energy (Beltrami and Haigh), shear (e.g. Tresca) or shear strain energy (Henckey & Von Mises)

Stress Amplitude (Sa)

Half the stress range (Sa = δS÷2)

Stress Block

A collection of characteristic identical stress ranges that represent a defined period of time in the fatigue life of a material or component

Stress Corrosion Cracking

The cracking or 'crazing' of a metal surface due to galvanic corrosion whereby the cracks generate stress-concentrations in the material weaking its ability to deform elastically

Hydrogen emrittlement is a typical example of this problem (see Cathodic Protection)

NACE MR0175/ISO 151546-1:2001(E) are internationally recognised standards that offer advice as to the control of this problem

Stress Cycle

One stress cycle is twice the stress range (e.g. maximum to minimum and back to maximum again)

Stress (mean)

Middle of the the stress range (Sm = (Ṡ+Ṣ)÷2)

Stress Range (δS)

The difference between the maximum stress and the minimum stress in a single stress cycle (δS = Ṡ-Ṣ)

Subduction

The passing of planet's crust under a tectonic plate and down into its mantle

Regions where this occurs are called Subduction Zones, and they are usually active with volcanoes and earthquakes

Substance

The bulk quantity of particles

(the) Sun

Diameter: 1.3914E+06 km
Surface area: 6.0821E+12 km²
Volume: 1.41044E+18 km³
Mass: 1.9885E+30 kg
Density (average): 1409.8437 kg/m³
Luminosity: 382.8E+24 J/s
Surface emission: 6.294E+07 J/m²/s
Surface temperature: 4400 K
Effective temperature: 5772 K
Core temperature: 1.571E+07 K

Principal constituent elements (99.998%):
Hydrogen: 90.965%
Helium: 8.889%
Oxygen: 0.0774%
Carbon: 0.0330%
Neon: 0.0112%
Nitrogen: 0.0102%
Iron: 0.0043%
Magnesium: 0.0035%
Silicon: 0.0032%
Sulphur: 0.0015%

The above figures are provided in NASA's Sun Fact Sheet

Surface Energy (US)

The free energy per unit area in a substance

US = surface tension x surface area
the units of measurement are J, Btu, N.m, lbf.ft, etc

Surface Tension

A property of liquids whereby their surface appears to have an elastic membrane in a state of tension
the units of measurement are N/m, dyne/cm, lbf/ft, etc

This phenomenon occurs at the surface of liquids due to unbalanced cohesive forces between surface molecules that do not occur in the bulk of the liquid where molecular cohesive forces are able to act in all directions.

Surge (vessels)

Surge

The linear movement of a vessel in the direction of the longitudinal ('x') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Sway (vessels)

Sway

The linear movement of a vessel in the direction of the lateral ('y') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Sweating
(metals together)

Line (or coat) the surfaces of two metals with melted solder or braze and allow to cool.
Subsequently press the two metals together whilst heating to a temperature sufficient to remelt the solder or braze.
Then allow to cool whilst under pressure.

System

Thermodynamic: A quantity of matter subjected to a process, everthing else is its surroundings
For example when evaluating steam in an autoclave, everything apart from the steam itself is its surroundings (including the pressure vessel and its environment)

Mechanical: The components that together create a particular action
For example a bicycle comprises the frame, wheels, chain and drive mechanism, brakes, handlebars and seat. Everything else (mudguards, paniers, basket, etc.) is an accessory.

Chemical: The molecules, atoms, sub-atomic particles and electro-magnetic radiation that are responsible for a chemical reaction
For example an oxygen atom (O), an oxygen molecule (O₂) and UV light that together create Ozone (O₃)

see Thermodynamics and Sub-atomic Physics

Tauon

A negatively charged elementary particle also referred to as a tau particle

The tauon and its anti-particle carry the same electric charges as the electron and positron respectively

A tauon is classified as a lepton

m=3.167469045E-24g [1.77682GeV/c²], lifetime≈2.9E-13s

Techtonic Plate

An area of planet crust that changes size and shape over time due to mantle activity

Normally, a length of the tectonic plate's perimeter (edge) grows through new rock generation from volcanic emissions and the remaining perimeter is subject to subduction

Temper

Tempering is carried out to increase toughness and ductility in a material that has been previously hardened.

The tempering process is carried out by heating the material to a temperature below its transformation temperature (1330°F or 723°C) and cooling in a controlled environment/manner to allow some recrystallisation to occur.
E.g. for carbon steel, the tempering range is 210°F (100°C) to 1200°F (650°C). The higher the tempering temperature, the greater the toughness and the lower the resultant hardness and strength.

Temperature

The degree of heat measured relative a particular scale
e.g. triple-point of fresh water and absolute zero

The two most commonly used 'absolute' scales are:
Kelvin (K):
0K is absolute zero and the triple-point of water is 273.15K
Rankine (°R):
0°R is absolute zero and the triple-point of water is 491.67°R
1°R = 5/9K

The two most commonly used 'non-absolute' scales are:
Celsius; also called centigrade (°C):
0°C is the triple-point of water and the boiling point of water at 1 atmosphere = 100°C
Fahrenheit (°F):
32°F is the triple-point of water and the boiling point of water at 1 atmosphere = 212°F
1°F = 5/9 x 1°C

To convert between scales:
X°F = Y°C x 9/5 + 32
Y°C = 5/9 x (X°F - 32)

0K = 0°R = -273.15°C = -459.67°F
255.37K = 459.67°R = -17.78°C = 0°F
273.15K = 491.67°R = 0°C = 32°F

Tensile Modulus

A general term that applies collectively to the resistance to axial deformation for all materials (e.g. metals, polymers, woods, etc.) including; Young's, flexural and elastic moduli.

Tetra-hedra

tetra-hedra

Describes the lattice arrangement of atoms within a metal.

The smallest crystal of this metal will contain four closely packed atoms, each of which are located at each corner of a tetrahedron.

Thermal Conductivity (k)

The rate at which heat flows through a material or substance of unit thickness.

see Thermal Conductivity-technical help

Thermal Resistance (R)

The temperature difference across a barrier of a specified thickness when a unit of heat flows through it in unit time.
The reciprocal of 'Heat Transfer Coefficient'
(R = 1/U)

see Thermal Conductivity-technical help

Thermodynamics

The theory of the transfer of energy between systems or its conversion into work

In other words ...
'it is the formulas and calculations used to identify the amount of heat energy that is transferred from one system to another or converted into mechanical, chemical or electrical action, and how much is lost to its surroundings, i.e. the efficiency of the process'

see Thermodynamics

Thermosphere

Stratum of the earth's atmosphere that contains the Ionosphere (Lower Thermosphere) and the Exosphere (Upper Thermosphere)

Thermosphere means 'hot region'. The temperature of this region increases exponentially with altitude but the density of material in this stratum is so thin that the heat generated cannot be readily transferred.

Through Harden

A process whereby the entire body of a steel alloy is hardened to the same extent and is normally achieved by the addition of alloying elements.

Top Quark

The most massive of all the quarks and part of the third generation of matter

The top quark is classified as a fermion

mᵣ=3.085252685E−22g [173.07GeV/c²], lifetime≈5E−25s, Q=⅔e, Iz

Torque

A rotational moment

This is a tangential force applied to a structural element at a given radial distance from the axis of twist.

Transfer Function
(ships)

see Response Amplitude Operator

Transformation Temperature

The temperature range during which austenite occurs during heating.

It is also a different temperature range during which Austenite disappears during cooling.

These temperature ranges may overlap but they are never the same.

Transformer (electrical)

A transformer is a single central magnet around which are wound two or more separate copper wire coils with a different number of turns.
One of the coils will be the input power supply and the other will be output power supply. Both supplies will have same power (Volts x Amps) if you ignore losses.

The voltage in each coil will vary thus: V2 / V1 = n2 / n1
So the largest number of turns will have the highest voltage but lowest current and vice-versa.

Transom

An horizontal (or transverse) structural member

Triangle

A two-dimensional, three-straight-sided closed shape the 3 angles of which add up to 180° (πᶜ)

Triple-Point of Water

273.16K, 0.01°C, 32.018°F & 491.688°R

The temperature at which pure water can exist in all of its phases (solid, liquid and gas) simultaneously at 1 atmosphere (pressure)

Trochoid (curve)

A trochoid curve

A trochoid is a curve generated by a point inside or outside the circumference of a circle that is rolled along a flat, straight surface.

see also Cycloid, Epicycloid and Hypocycloid

Troposphere

The ceiling for 75% of nitrogen, the earth's most abundant atmospheric gas

Altitude @ equator: 0km to 15km
Altitude @ poles: 0km to 10km

Weather generating stratum of the earth's atmosphere that contains all of the earth's gases

Temperature reduces with increasing altitude

True Power (electrical)

True power is the apparent power multiplied by the power factor and is normally expressed in terms of 'W' or 'kW'.

see also Alternating Current and Phase Angle

Turbulent Flow

A flowing fluid that disturbs and mixes adjacent layers

Uncertainty Principle
(Heisenberg)

Any pair of dimensional variables (e.g. time and energy) describing a sub-atomic particle cannot be determined to an accuracy whereby the product (multiplication) of the errors (of each variable) is less than Dirac's constant

E.g.: the more precisely the position of a particle is determined the less precisely its momentum can be known, and vice-versa

Upheaval Buckling (pipeline)

Lateral displacement of a pipeline due to uncontrolled longitudinal compression.

Upheaval Buckling-technical help
see also End Cap (force)

Up Quark

One of the two types of quark that make the proton and the neutron and forms part of the first generation of matter

The up quark is classified as a fermion

mᵣ=3.565323494E-27g [2.01MeV/c²], Q=⅔e, Iz

Ultimate Tensile Stress
(UTS)

The maximum stress a material will support before it begins to suffer internal fracturing

Resistance to deformation (strength) is increased between yield stress and ultimate tensile stress through work hardening

The gradual reduction in strength after reaching UTS is due to increasing internal fracturing which will continue to reduce until the material breaks

Utilisation

The proportion of limiting stress (or use) you design into a component before its material fails.

For example: if you design a component to experience a maximum design stress of 200 N/m² and the material from which it has been manufactured has a minimum specified yield stress of 400 N/m², the component has a utilisation of 0.5

Utilisation is the inverse of safety factor

Vacuum

A volume greater than zero that contains no matter
i.e. no sub-abtomic or atomic particles of any kind

Valence Shell
(of an atom)

The outermost shell of an atom in which an electron exists and includes all sub-shells

The valence shell represents an atom's bonding capacity and hence defines its chemical properties.

Vapour

A liquid in a gaseous state

Vector (V)

A straight line action (e.g. force) that has both magnitude and direction

see also Polar Co-Ordinates and Cartesian Co-Ordinates

Velocity (v)

Constant rate of change in distance (distance ÷ time)

Vertex (Vertices)

The point at which one end of each of two lines connect

Vibration

The elastic reponse of a sprung system to repeated loads of similar magintude and frequency

Virtual Mass
(fluidics)

A shape coefficient that represents the sum of the fluid displaced by the body and the added mass of the surrounding fluid dispursed by the body and its displaced mass
also know as Inertia Coefficient

see Added Mass & Drag

Viscosity

Viscosity is the measurement of a fluid's resistance to shear, and therefore to flow. It is the tangential force per unit area necessary to maintain a unit relative velocity between two parallel planes.

Kinematic viscosity (ν) is measured in units of m²/s, although it is most commonly measured in Stokes (St) or centiStokes (cSt) where 1m²/s = 1000St

Dynamic (or absolute) viscosity (μ) is the kinematic viscosity multiplied by the mass density (ρ) of the fluid and has the units of kg/s/m (or N.s/m²), although it is more commonly measured in Poise (P) or centipoise (cP) where 1N.s/m² = 10P

Voltage (V)

The potential difference between two sources of electrical energy (the unit of measurement is the Volt). Also known as potential difference (pd) and electro-motive force (emf)

The pipeline analogy for voltage is the pressure drop across the inlet and outluet of a pipe with a fluid flowing through it.

V = I.R
also;
1 V = 1 J/C
1 eV = 1.60217648753E-19 J/C

Vortex Shedding

Vortex Shedding

The generation of 'vortices' (rotating fluid) in the wake of a fluid passing over an object

see Vortex Shedding-technical help

W Boson

A weak force carrier

There are two types of W Boson
(one with an electric charge of +1e and the other with an electric charge of –1e)

Wˉ is the anti-particle of W⁺

m=1.4332244E−22g [80.398GeV/c²], lifetime≈3E-25s, Q=±1e, Iz=1

Wavelength

The speed of a wave divided by its frequency

Wave Number

The reciprocal of wavelength
wavenumber = frequency

Weak Force

An interaction between elementary particles that is responsible for certain decay processes (such as beta radiation) and acts upon all known fermions

Particles interact through the weak force by exchanging W & Z Bosons, which are heavy (≈100 times that of a proton). Their mass defines the short-range (≈1E-17m or ≈100 times less than the diameter of a typical atomic nucleus) nature of the weak force and that makes the weak force appear weak at the low energies associated with radioactivity.

Weather Window

A period of time during which limiting weather conditions will not be exceeded

i.e.; A large weather window means a long period of time over which these limiting conditions are not expected to be exceeded

conversely; A small weather window means a short period of time over which these limiting conditions are not expected to be exceeded

Weight

The resultant force between two bodies as a result of gravitational acceleration and is measured in N, pdl, etc.

The weight of a body is equal to its mass multiplied by the gravitational acceleration.

This property varies with gravitational acceleration. That is, any given mass will weigh differently on the Earth and the Moon, both of which have different gravitational accelerations. Out in deep space, away from all gravitational effects, a mass of 1 tonne will weigh nothing!

Weld Joint Factor (WJF)

A utilisation factor for the strength of a welded joint

A weld joint factor of 1.0 is usual for coded welders using certified procedures and materials

The lowest WJF for a weld completed by an experienced, but uncoded welder using uncertified procedures and materials is ≈0.6
WJFs less than this are normally associated with unreliable welds.

Wire Rope

A rope comprising at least one strand, which comprises more than one filament made from metal

Also recognised generically as: wire, steel rope, multi-strand wire, flexible wire, cable, cord and steelcord

see Wire Rope-technical help

Work

A quantity synonymous with energy

Mechanical: a force applied over a distance greater than zero
Electrical: power (W, J/s) multiplied by the duration (seconds)
Thermo-Chemical: specific heat capacity multiplied by the mass and multiplied by the temeprature of a system

The greater the force or the further the distance the more work has been done

The units of measurement are; Btu, W.h, J, cal, N.m, lbf.ft etc.

Work Harden

The process of through-hardening a steel or a steel alloy by repeated deformation at stresses greater than yield stress

However, if the steel/alloy is subsequently held at a sufficiently high temperature for a long enough period it will eventually revert to its original properties

Wrap
(wire rope)

The longitudinal helical coiling of filaments into strands or strands into wire rope during the manufacturing process
see also Lang Lay and Regular Lay

X-Rays

Short-wave electromagnetic radiation that falls between ultra-violet light and gamma radiation

Ranges from:
1.0E-10m < λ < 1.0E-08m
(2.99792459E+18Hz > ʄ > 2.99792459E+16Hz)

Yaw (vessels)

Yaw

The rotational movement of a vessel about the vertical ('z') axis

Whilst this term generally applies to the movement of ships, it is also used to define the movement of any object subject to the same degrees of freedom; e.g. aircraft and spacecraft

see Right-Hand Rule for positive and negative directions of this movement

Yield Stress

The maximum stress that can be applied to a metal whilst that continues to obey Hooke's Law

The release of stress above yield stress will result in permanent deformation of the material

see also Specified Minimum Yield Stress

Young's Modulus (E)

The linear relationship (the slope of the curve) between purely elastic stress and strain in a material
i.e. a material that obeys Hooke's Law

Z Boson

A weak force carrier

There is one type of Z Boson, which only changes spin and momentum but cannot change either electric charge nor any other charges (like strangeness, charm, etc.), so it never changes the generation or flavour of the particle emitting it.

The Z boson (or 'Z') is electrically neutral and is its own anti-particle

m=1.62556647E−22g [91.1876GeV/c²], lifetime≈1E-25s, Q=0, Iz=1

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