GATE ME 2017 Set 1 — Question 6
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Fluid Mechanics → Fluid Kinematics & Dynamics → Continuity & Momentum Equations
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Question
For steady flow of a viscous incompressible fluid through a circular pipe of constant diameter, the average velocity in the fully developed region is constant. Which one of the following statements about the average velocity in the developing region is TRUE?
Correct answer
(B) It is constant and is equal to the average velocity in the fully developed region.
Solution
According to the continuity equation for steady, incompressible flow in a pipe of constant cross-sectional area , the mass flow rate is constant:Since the fluid is incompressible ( is constant) and the pipe diameter is constant ( is constant), the average velocity must remain constant throughout the entire length of the pipe. While the velocity profile changes from a uniform profile at the entrance to a parabolic profile in the fully developed region, the average velocity across any cross-section remains the same to satisfy conservation of mass.
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