What is the difference between a Forced Vortex and a Free Vortex ?

A vortex is a rotation of the flow about an axis or a curved line.  Vortices are formed either naturally or can be forced.

A Free vortex requires no external torque.  It occurs when the water drains out of a tank or container.  In a free vortex, the velocity is lowest in the outer periphery and it progressively increases towards the centre.  Thus, the velocity profile is inversely proportional to the radius of the vortex.

A Forced vortex is formed when an external torque is applied.  An example would be fluid rotated by a pump impeller.  In a forced vortex all the particles are at the same velocity.