GATE ME 2017 Set 1 — Question 31
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Fluid Mechanics → Viscous & Pipe Flow → Darcy-Weisbach & Moody Diagram
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Question
Consider steady flow of an incompressible fluid through two long and straight pipes of diameters and arranged in series. Both pipes are of equal length and the flow is turbulent in both pipes. The friction factor for turbulent flow though pipes is of the form, , where and are known positive constants and is the Reynolds number. Neglecting minor losses, the ratio of the frictional pressure drop in pipe 1 to that in pipe 2, , is given by
Correct answer
(A) ((d₂)/(d₁))⁽⁵⁻ⁿ⁾
Solution
The frictional pressure drop in a pipe is given by Darcy-Weisbach equation:For pipes in series, the volumetric flow rate is constant. Velocity .
The Reynolds number is .
The friction factor is given as .
Substituting these into the pressure drop equation:Thus, the ratio of pressure drops is:Therefore, the correct option is (A).
The Reynolds number is .
The friction factor is given as .
Substituting these into the pressure drop equation:Thus, the ratio of pressure drops is:Therefore, the correct option is (A).
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