Chemical Engineering - Fluid Mechanics - Discussion

The radial component of velocity is the same everywhere.

The Correct assumption in the idealized free vortex.
In a free vortex, the radial component of velocity vr​ is assumed to be zero.
The only non-zero component is the tangential velocity vθ​ .

Vortex flow:

The motion of a fluid in a curved path is known as vortex flow.

When a cylindrical vessel containing some liquid is rotated about its vertical axis, the vortex flow will be followed by liquid.
Vortex motion is of two types:

1. Forced vortex:

In the forced vortex, fluid moves on the curve under the influence of external torque. Due to the external torque, a forced vortex is a rotational flow. As there is a continuous expenditure of energy, Bernoulli's equation is not valid for forced vortex.
For forced vortex, v = rω is applicable.
Examples: The flow of water through a runner of the turbine.Rotation of water in the washing machine.

2. Free vortex:

When no external torque is required to rotate the fluid mass, that type of flow is called a free vortex. As there is no torque in the free vortex, so free vortex is an irrotational flow.
For a free vortex, a moment of momentum is constant i.e. vr = constant.
Examples: The flow of liquid through a hole provided at the bottom of a container.Draining the bathtub.

So, the vortex flow is both rotational and irrotational flow depending on the torque applied.