• Second moment of area moment of inertiaSecond area moment calculation 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 database3 Engineering Principles calculation4 Trigonometry calculation5
access to the technical calculator
Q & A General 2ᴺᴰ Moment of Area 2ᴺᴰ Moment of Area+ Added Mass & Drag Areas & Volumes Balancing (rotary) Beam Strength Beam Strength+ Bearings (low friction) Bearings (plain) Bending Moments BiMetallic Strip Buoyancy Carbon Steel Catenary Catenary+ Cathodic Protection Centrifugal Force Colebrook & Fanning Column Buckling Combined Stress Co-ordinates Copper Alloys Electrical Current Elliptical Curves Engineering Basics Explosions Fans Fatigue Flange Gaskets Flanges Floors Fluid Forces Fluid Numbers Friction Galvanic Corrosion Gears Hardness Conversion HPHT Flexible Pipe Lift Rigging Logs & Trig Machining Tolerances Metal Properties Mode Shapes Ocean Waves Padeyes Partial Pressures Piling Pipe Flow Pipe Flow+ Pipe Strength Plastic Stress in Beams Plate Deflection Pressure Vessels Reel Capacity Resolution of Forces Screw Thread Machining Screw Threads Shafts Shock Loads Spring Coefficients Spring Strength Steel Beam Sizes Stress Concentration Table of the Elements Thermal Conductivity Trigonometry UniQon Upheaval Buckling Velocity & Acceleleration Vessel Motions Vessel RAOs Vibration Damping Vortex Shedding Walls, Barriers & Tanks Weight Lifting Welding Wire Rope

Q&A forum: Centrifugal and Axial Fan Calculator

All relevant questions concerning this program will be posted here along with our answers for everyone to view.
Please forward your questions to info@calqlata.com or visit our Contact Us page.

The rule of thumb "one impeller volume per revolution" has been called in to question ...

As a result of this question, CalQlata successfully carried out an internal verification based upon the energy required to shift such a mass.

Whilst it was considered prudent to re-issue the 'Fans' calculator now calculating the impeller speed (RPM) required to generate an entered value for volumetric flow rate based upon the required energy;
the aforementioned rule of thumb still applies.

Unfortunately, I am not a fan expert either! The power and pressure seem OK, but the flow rate is the problem.

We have measured directly the flow rate and although there are obviously some errors in measurement, we seem to have broadly similar practical results of less than 1m3/s. What I really would like to know is the accuracy of the 'rule of thumb' (effective rotor volume x rpm), which I cannot seem to corroborate on a google search.

Does the calculator just produce this value regardless of any other input values?

The standard theory on centrifugal fans was generated by Charles H Innes in 1916 ("The Fan"), and it appears to have stood the test of time.
His theory is based upon the aerodynamics of the blade transferring air from the toe of the blade to the outer lip in a single revolution of the impeller.
He also states that the greater the number of blades the more uniform the flow; i.e. more of the airflow will be laminar (less turbulent). An infinite number of blades will generate the most uniform flow. However, he also states that this comes with increased skin friction.
At some point the losses from skin friction will exceed the inlet and outlet losses and a compromise is needed.
Innes suggests that six blades is the best for a low aspect ratio (<0.67) increasing to twelve blades for aspect ratios approaching one.
This recommendation is based upon his own (extensive) experience.

Twelve blades, however, may not be suitable for very large diameter impellers of high aspect ratios.
In my own (less extensive) experience, I have settled for five blades for aspect ratios of 0.5 increasing to an inlet pitch of similar dimension to the radial depth of the blade.
I would multiply the skin friction in the calculation by the number of blades and would also use a higher value than that suggested by Innes for frictional resistance (0.125) on the basis that 'used' fan blades (that have been in service for some time) will have slightly eroded surfaces (i.e. 0.15 to 0.2).
With regard the expected accuracy of the calculator, if Innes is correct, then the calculations in CalQlata's Fans calculator should be ±0%. But I would only consider this to be the case for properly designed impellers in dry air. Moisture in the air (>1%) can cause a reduction in efficiency. In normal everyday conditions, with a used fan that has been properly designed and maintained, I would expect an accuracy better than ±10% (i.e. ±4% to ±8%), but this does not include the effects of the inlet and outlet diffusers, which can improve or reduce the impeller's effective efficiency.

I (personally) have never seen a fan deliver more than its impeller volume per revolution unless the atmospheric outlet pressure is less than the inlet pressure (an effective vacuum). Therefore, I am unable to refute Innes' theory. I am happy, however, to leave this debate open to anybody that can show Innes' theory to be incorrect. Please let us know if you can do this mathematically and supported with practical evidence.

Can you comment on the limitations of the equations that were implemented in this software? Specifically with regards to impeller size. I’m investigating design changes on a relatively small impeller (3-4”), and so far this software is predicting an output flow that is much higher than has been empirically captured. Any feedback would be appreciated.

The theories in the calculator are correct for all sizes, i.e. for fans with impellers smaller than a millimetre to greater than 10m.
The problem with ever decreasing size is friction.

As your fan gets smaller the ratio of surface area with volume increases, and the smaller it gets the greater this ratio becomes.
If we use a pipe as an analogy:
Dia   Area               Volume           A:V        δε
24   150.7964474   1809.557368   0.083
23   144.5132621   1661.902514   0.087   4.167%
22   138.2300768   1520.530844   0.091   4.348%
21   131.9468915   1385.442360   0.095   4.545%
20   125.6637061   1256.637061   0.100   4.762%
19   119.3805208   1134.114948   0.105   5.000%
18   113.0973355   1017.876020   0.110   5.263%
17   106.8141502   907.9202769   0.120   5.556%
16   100.5309649   804.2477193   0.125   5.882%
15   94.24777961   706.8583471   0.13 0  6.250%
14   87.9645943   615.75216010   0.143   6.667%
13   81.68140899   530.9291585   0.154   7.143%
12   75.39822369   452.3893421   0.167   7.692%
11   69.11503838   380.1327111   0.180   8.333%
10   62.83185307   314.1592654   0.200   9.091%
 9   56.54866776   254.4690049   0.220   10.000%
 8   50.26548246   201.0619298   0.250   11.111%
 7   43.98229715   153.9380400   0.286   12.500%
 6   37.69911184   113.0973355   0.330   14.286%
 5   31.41592654   78.53981634   0.400   16.667%
 4   25.13274123   50.26548246   0.500   20.000%
 3   18.84955592   28.27433388   0.670   25.000%
 2   12.56637061   12.56637061   1.000   33.333%
 1   6.283185307   3.141592654   2.000   50.000%

In this case ‘δε' represents the increase in inefficiency over the previous size
As A:V increases the ratio of surface area to volume increases, and this increase is exponential. As you can see from the table when the pipe size falls to 3" the increase becomes rapid. Look at the difference between a 24" to 23" (4%) and that for 4" to 3" (25%)

Surface friction has a far greater effect on efficiency in a fan than it does in a pipe because the ratio of surface area (contact surface) is greater than in a pipe. Therefore, a similar table to that above for fans would show an even more marked increase at smaller diameters.

Centrifugal fans are less suited to smaller diameter for a number of reasons.
1) The surface area in contact with the flowing air is greater than for axial fans
2) The air is forced to change direction
3) The shape of the inlet and outlet ducts is not best suited for reducing frictional losses (circular is better than rectangular)

This is why centrifugal fans tend to be targeted for larger fans and axial configurations for smaller diameters
I am not saying you shouldn't try to design a small centrifugal fan if that best suits your purposes, simply that you take extreme care in its design. For example, the following should be considered:
1) Use a material with a very low surface friction (or coat the material, but bear in mind that the loss of the coating during the design life will result in a loss of efficiency).
2) Reduce the number of blades
3) Minimise the surface area of material in contact with the flowing air
4) Eliminate sudden changes in shape

For what it’s worth, if I were designing a very small high-performance fan, I would start with a multistage axial configuration (along with suitable venturies if I was looking for pressure as opposed to flow).

Follow-Up Email:

I believe that your input/output data is based upon the following units:
Input Data:
θᵢ,   45 {°}
θₒ,   120 {°}
Øᵢ,   0.02 {m}
Øₒ,   0.075 {m}
w,   0.01 {m}
ρᵢ,   1.165 {kg/m³}
pᵢ,   101322.5 {N/m²}
Ṯ,   291 {K}
g,   9.80663139 {m/s²}
Rₐ,   8.3143 {J/K/kg}
F,   0.125
N,   7000 {RPM}
Output Data:
Q,   0.004788 {m³/s} [287.28 l/min]
H,   38.207032 {m}
δp,   436.50484 {N/m²}
pₒ,   101,759.00 {N/m²}
ρₒ,   42.058538 {kg/m³}
ε,   47.55515 {%}
T,   0.002851 {N.m}
P,   4.394551 {N.m/s}
A,   0.001486 {m²}
v,   3.221569 {m/s}
Lˢ,   0.00427 {m}
Lᶠ,   0.035085 {m}
Lᵉ,   42.096188 {m}
vᵢ,   7.625286 {m/s}
vₒ,   28.734015 {m/s}
v₁ᵢ,   7.619792 {m/s}
v₁ₒ,   2.031945 {m/s}
v₂ᵢ,   7.330382 {m/s}
v₂ₒ,   27.488935 {m/s}
v₃ᵢ,   10.776012 {m/s}
v₃ₒ,   2.346287 {m/s}
v₄ᵢ,   -0.289409 {m/s}
v₄ₒ,   28.662079 {m/s}

With regard to your concerns about flow rate:
Q = 0.004788m/s = 287.28 l/min
A very good rule of thumb for any fan is that its impeller will pass its (contained) volume of air in one revolution.
If I apply this argument to the volume of your impeller, I get: 287.2593783 l/min
So the calculator and the rule of thumb both appear to be working correctly.
However, the above would only be achievable if chamber, impeller, inlet and outlet designs added nothing to the losses#. As mentioned before, their influence becomes significantly greater as the size of the fan reduces. Like you, I would expect closer to 100 l/min for a centrifugal pump of the size you are designing unless all aspects of the fan design were perfect in every way. In fact, even with the best possible materials and designs, I would not expect see better than 200 l/min for such a small (centrifugal) fan
With larger fans (i.e. 6" and greater), it should be much easier to achieve the calculated values.

May I venture a couple of comments on the input data?
The value of Rₐ is for the specific gas constant;
Rₐ (Rᵢ/RAM) = 283.5312934 J/K/kg
as opposed to ideal gas constant;
Rᵢ = 8.3143 J/K/mole
You can see how we use these symbols in our definitions page {http://calqlata.com/help_definitions.html > Gas Constant}
The differences you will notice are in outlet density {ρₒ}, the minimum area diffuser requirement {A} and all the velocities {v}

The recommended angle for the blade inlet should be used where possible as you will see improvements in efficiency, outlet pressure, outlet velocity and power consumption. Whilst I agree that such improvements are very small between 45° to 46.109°, every little helps when attempting to minimise defects (for such small fans).

I notice that the outlet angle (120°) has turned the blades from backward facing to forward facing (see http://calqlata.com/productpages/00060-help.html Fig 3). I am not sure if this was intentional (special requirements) but the smaller the outlet angle for a backward facing blade, the better its efficiency.
Using your customer’s input data with θᵢ = 46.109° and θₒ = 8° the efficiency increases from 47.5% to 72% and the power required to run the fan drops from 4.4W to 2W. Whilst you lose head and pressure the efficiency gain is greater than the loss.
By setting the outlet angle (θₒ) to 25° you achieve virtually the same head and pressure but with an efficiency of over 57% and a drop in power consumption of 25%

# Note: the efficiency quoted (ε {%}) is for blade design only

I have a question regarding the power and torque calculation in your fans software. I expected that Power = torque * rotational velocity. So per the below, rotational velocity = 1099.6 rad/s (RPM * 2*pi/60) and power should equal 2.97W. The program is outputting a power of 4.49W. What is causing this discrepancy? Please let me know when you have a moment.

The torque you get from Fans’ output data is that required to generate the airflow (Q)
The power you get from Fans is that required to generate the Torque which will be dependent upon the efficiency of the system (ε)
Therefore, in order to generate the airflow (Q) you will need to apply more power than would be required theoretically:
i.e. 2.9364 / 66% = 4.49 (Q/ε)

CalQlata™ Copyright ©2011-2016 CalQlata info@calqlata.com Site Map Terms of website use Our Store