GATE ME 2015 Set 1 — Question 16
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Fluid Mechanics → Viscous & Pipe Flow → Darcy-Weisbach & Moody Diagram
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Question
Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of
Correct answer
(D) 64
Solution
The head loss due to friction in a pipe is given by the Darcy-Weisbach equation:The velocity can be expressed in terms of the mass flow rate :Substituting into the head loss equation:Given that the friction factor , mass flow rate , and density are constant:If the length is doubled () and the diameter is halved ():Therefore, the head loss increases by a factor of 64.
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