GATE ME 2016 Set 3 — Question 49
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Fluid Mechanics → Viscous & Pipe Flow → Parallel Plate & Hagen-Poiseuille
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Question
Consider a fully developed steady laminar flow of an incompressible fluid with viscosity through a circular pipe of radius . Given that the velocity at a radial location of from the centerline of the pipe is , the shear stress at the wall is , where is __________
Correct answer
2.6 to 2.7
Solution
For fully developed laminar flow in a circular pipe, the velocity profile is parabolic:
Given :
The shear stress is given by Newton's law of viscosity:
At the wall ():
Substituting :
Comparing with , we get .
Given :
The shear stress is given by Newton's law of viscosity:
At the wall ():
Substituting :
Comparing with , we get .
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