Project ForgeWhich 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 the entire flow field.
- AP and Q
- BR and S
- P and R
- DP and S
Explanation
A forced vortex is rigid-body rotation (v=ωr): shear stress is zero everywhere since there's no relative deformation between fluid layers (P true), and velocity is directly proportional to radius by definition (R true). But vorticity is a CONSTANT NONZERO value (2ω) everywhere — that's exactly what distinguishes a forced vortex from a free/irrotational vortex (Q false). Total mechanical energy is also NOT constant across the flow field (it increases with r² due to the radial pressure gradient balancing centrifugal effects, unlike a free vortex which does satisfy Bernoulli across streamlines) (S false). Correct: P and R.
Source: GATE ME 2007 (2007)
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