GATE ME 2019 Set 2 — Question 33
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Fluid Mechanics → Viscous & Pipe Flow → Viscous Incompressible Flow
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Question
Water enters a circular pipe of length m and diameter m with Reynolds number . The velocity profile at the inlet of the pipe is uniform while it is parabolic at the exit. The Reynolds number at the exit of the pipe is ______.
Correct answer
500 to 500
Solution
The Reynolds number for flow in a pipe is defined as , where is the density, is the average velocity, is the diameter, and is the dynamic viscosity. For steady, incompressible flow in a pipe of constant diameter, the mass flow rate is constant. Since and are constant, the average velocity must remain constant throughout the pipe, regardless of the shape of the velocity profile (uniform at inlet, parabolic at exit). Therefore, the Reynolds number at the exit is the same as at the inlet: .
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