Vortices Calculator v1

Subject

A vortex is a spiralling body of fluid, the properties of which may be mathematically predicted using just a few basic inputs.

Free (or natural) vortices are a function of the natural forces prevalent at the surface of our planet. Perform the same experiment on Mars, for example, and the vortex will behave differently. Whilst a free vortex may be used for practical purposes, the inherent forces and energies available are normally insufficient to drive heavy equipment.

Forced (or artificial) vortices are generally induced to drive pumps and generators. They are analogous to old fashioned water-wheels that use natural flow to drive rotary equipment that may be almost any practical power rating; e.g. hydro-power (dams).

Bernoulli’s equations may be applied to both free and forced vortices to identify downstream or upstream fluid linear performance.

The vortex calculator includes a calculation option for Bernoulli’s equation to provide the common input data for the other three calculation options. Whilst the fluid properties entered here are carried forward to the other three calculation options, its primary function is to provide fluid power via a riser for a forced vortex, for those that wish to calculate it.

Vortices includes two vortex calculation options; Free and Forced, both of which calculate the performance properties of the spiralling fluid together with the surface profile data that may be plotted in a spreadsheet.

In addition to the above calculation options, Vortices also provides a classical calculation facility for 'falling spheres', which are frequently used for the measurement of fluid flow in a pipe.

For help using this calculator see Technical Help

Vortices Calculator - Options

Bernoulli

This calculation option is for the properties of a fluid passing through a duct, such as a pipe. It also provides the basic (common) data - fluid density, viscosity, gravitational acceleration, etc. - for the other calculation option.

You enter:	and the vortices calculator will provide:
internal diameter (pipe) length (pipe) inlet head inlet altitude outlet altitude outlet pressure kinematic viscosity fluid density gravitational acceleration	internal area (pipe) volumetric flow rate inlet pressure inlet velocity outlet velocity outlet force outlet energy outlet power Reynold's number friction head loss friction coefficient pressure loss

Forced Vortex

This calculation option is for the properties of a forced (or artificial) vortex. The fluid properties are carried over from the Bernoulli calculation option and 'p' is any point in the vortex.
In addition to the calculation results listed below, this option also provides the co-ordinates for plotting; 'radius', 'tangential velocity', 'surface profile'.

You enter:	and the vortices calculator will provide:
radius to point 'p' depth to point 'p' inside radius outside radius static head inlet flow rate	angular velocity surface elevation @ 'Rₒ' minimum height maximum height height @ 'r' tangential velocity @ 'r' centrifugal acceleration @ 'r' centrifugal pressure @ 'r' gravitational pressure @ 'd' vorticity hydrostatic condition

Free Vortex

This calculation option is for the properties of a free (or natural) vortex. The fluid properties are carried over from the Bernoulli calculation option and 'p' is any point in the vortex.
In addition to the calculation results listed below, this option also provides the co-ordinates for plotting; 'radius', 'tangential velocity', 'air-cone profile'.

You enter:	and the vortices calculator will provide:
radius to 'p' depth to 'p' outlet radius (rₒ) head @ 'rₒ'	tangential velocity @ 'rₒ' tangential velocity @ 'r' centrifugal pressure @ 'r' gravitational pressure @ 'd' pressure differential @ 'r' and 'd' constant of motion vorticity

Falling Spheres

This calculation option is intended to determine the velocity of a fluid that will stop a sphere from falling (measuring fluid flow). The fluid properties are carried over from the Bernoulli calculation option.

You enter:	and the vortices calculator will provide:
internal diameter (pipe) sphere diameter sphere density	flow type terminal velocity sphere mass fluid force on sphere drag coefficient Faxen-Oseen factor Reynold's number

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