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Fluid Mechanics
Flow Through Pipes
GATE 2013
Medium

An incompressible Newtonian fluid, filled in an annular gap between two concentric cylinders of radii R1 and R2 (R1<r<R2), is flowing under steady state conditions. The outer cylinder rotates with angular velocity Ω while the inner cylinder is stationary. Given that (R2−R1)≪R1, the profile of the θ-component of the velocity Vθ can be approximated by

  • AR2Ω
  • B[(r−R2)/(R2−R1)]·rΩ
  • C[(r+R1)/(R2+R1)]·R1Ω
  • [(r−R1)/(R2−R1)]·R2Ω

Explanation

For a very thin gap ((R2−R1)≪R1), the flow is well approximated by planar Couette flow between two flat plates: a linear velocity profile from 0 at the stationary inner surface (r=R1) to the outer surface speed R2Ω at r=R2. This gives Vθ(r)=[(r−R1)/(R2−R1)]·R2Ω.

Source: GATE CH 2013 (2013)

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