The relation between tangential velocity (v) and radius (r) is given by:

Forced vortex flow: 

• Forced vortex flow is defined as that type of vortex flow, in which some external torque is required to rotate the fluid mass. The fluid mass in this type of flow rotates at constant angular velocity (w)

V = rw ⇒ w = V/r = constant

Free vortex flow: 

• When no external torque is required to rotate the fluid mass, that type of flow is called free vortex flow. In free vortex, rate of change of angular momentum = 0

Angular momentum = m × v

Moment of momentum = m × v × r

For free vortex × \(\frac{d}{{dt}}\left( {mvr} \right) = 0\)