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 waterwheels that use natural flow to drive rotary equipment that may be almost any practical power rating; e.g. hydropower (dams).
Bernoulli’s equations may be applied to both free and forced vortices to identify downstream or upstream fluid linear performance.
Calculator
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 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 coordinates for plotting; 'radius', 'tangential velocity', 'surface profile'.
You enter: 
and the vortices calculator will provide: 


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 coordinates for plotting; 'radius', 'tangential velocity', 'aircone profile'.
You enter: 
and the vortices calculator will provide: 


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: 


flow type

terminal velocity

sphere mass

fluid force on sphere

drag coefficient

FaxenOseen factor

Reynold's number

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