GATE ME 2015 Set 2 — Question 50
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Fluid Mechanics → Viscous & Pipe Flow → Parallel Plate & Hagen-Poiseuille
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Question
The head loss for a laminar incompressible flow through a horizontal circular pipe is . Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is . The ratio is
Correct answer
(C) 8
Solution
For a fully developed laminar flow in a circular pipe, the head loss is given by the Hagen-Poiseuille equation:where is dynamic viscosity, is pipe length, is average velocity, is density, is acceleration due to gravity, and is pipe diameter.Since the fluid () and pipe length () remain the same, we have:Let the initial state be and the final state be . We are given:
The ratio of head losses is:Thus, the correct option is (C).
The ratio of head losses is:Thus, the correct option is (C).
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