Which combination of the following statements about steady incompressible forced vortex flow is correct ? P.  Shear stress is zero at all points in the flow. Q.  Vorticity is zero at all points in the flow. R.  Velocity is directly proportional to the radius from the centre of the vortex. S.  Total mechanical energy per unit mass is constant in in the entire flow.

Which combination of the following statements about steady incompressible forced vortex flow is correct ? P.  Shear stress is zero at all points in the flow. Q.  Vorticity is zero at all points in the flow. R.  Velocity is directly proportional to the radius from the centre of the vortex. S.  Total mechanical energy per unit mass is constant in in the entire flow. Correct Answer P and R

Explanation:

• Forced vortex flow is that type of flow in which some external torque is required to rotate the fluid.
• For this type of flow

⇒ V = ωr

where,

V = velocity, ω =  angular velocity, r = radius

• In forced vortex motion, after initial transients, the liquid will move as a rigid body together with the container. There is no deformation, and thus there can be no shear stress, and every fluid particle in the container moves with the same angular velocity.
• The total mechanical energy changes with the radius. The total mechanical energy is the sum of pressure, kinetic and potential energy and is constant along a streamline but not in the entire flow. 
• To maintain a forced vortex flow, mechanical energy has to be spent from outside and thus an external torque is always necessary to be applied continuously.