GATE ME 2014 Set 3 — Question 55
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Fluid Mechanics → Viscous & Pipe Flow → Darcy-Weisbach & Moody Diagram
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Question
A fluid of dynamic viscosity kg/m.s and density kg/m flows with an average velocity of m/s through a long duct of rectangular ( mm mm) cross-section. Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______
Correct answer
1.7 to 2
Solution
1.Calculate the hydraulic diameter ():
For a rectangular duct of dimensions :Given mm m and mm m:
m
2.Calculate the Reynolds number ():
Since , the flow is laminar.
3.Calculate the pressure drop ():
For laminar flow in a rectangular duct with aspect ratio , the friction factor constant .The pressure drop per unit length () is given by the Darcy-Weisbach equation:
Pa/mThe calculated value falls within the range to .
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