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Fluid Mechanics
Flow Through Pipes
GATE 2019
Hard

An incompressible Newtonian fluid flows in a pipe of diameter D1 at volumetric flow rate Q. The same fluid flows in another pipe of diameter D2=D1/2 at the same flow rate Q. The laminar entrance (transition) length is l1 for D1, l2 for D2. The ratio l1/l2 is

  • A1/4
  • 1
  • C2
  • D4

Explanation

Entrance length Le=0.05·Re·D, with Re=4ρQ/(πμD)∝1/D at fixed Q. So Le=0.05D×(const/D)=const, independent of D. Thus l1=l2, ratio=1.

Source: GATE CH 2019 (2019)

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