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Fluid Mechanics

Q1: For the laminar flow of a fluid in a circular pipe of radius R, the Hagen-Poisseule equation predicts the volumetric flow rate to be proportional to

A R

B R2

C R4

D R0.5

ANS:C - R4

For laminar flow of a fluid in a circular pipe, the Hagen-Poiseuille equation predicts that the volumetric flow rate QQQ is proportional to the fourth power of the radius RRR of the pipe. The Hagen-Poiseuille equation for laminar flow through a pipe is given by: Q=πR4ΔP8μLQ = \frac{\pi R^4 \Delta P}{8 \mu L}Q=8μLπR4ΔP​ where:

  • QQQ is the volumetric flow rate,
  • RRR is the radius of the pipe,
  • ΔP\Delta PΔP is the pressure drop across the pipe,
  • μ\muμ is the dynamic viscosity of the fluid,
  • LLL is the length of the pipe.
From this equation, we see that QQQ is directly proportional to R4R^4R4. Therefore, the volumetric flow rate QQQ is proportional to R4\boxed{R^4}R4​ for laminar flow in a circular pipe according to the Hagen-Poiseuille equation.



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