Forced Vortex Flow
When there is external torque is applied to the flow to rotate the flow then it is called as a forced vortex flow.
ω = constant
v/r = constant
Example: Fluid inside the centrifugal pump or fluid is in a container and container is being rotated around its axis
Free Vortex Flow
In this kind of flow external torque is zero i.e. no external torque is applied.
Example:Flow in a circular pipe or A whirlpool in river.
First of all, let’s take a general case where the fluid is rotating about some axis and we will find an expression for the pressure at some point.
Let us consider a small element of fluid element rotating at uniform velocity in horizontal plane about an axis perpendicular to out of plane.
∂P/∂r is a pressure gradient.
If it is positive then pressure increases with radiaus and if it is negative pressure decreseas with radius
But we already know that pressure variation in vertical plane is given by hydrostatic law, as
∂P/∂h = ρg
Hence, it can be said that pressure at any point is function of h and r
P = f(r,h)
The pressure difference between two points can be calculated with the help of the integrating function.