Fluid mechanics - Poiseuille Equation

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SUMMARY

The discussion focuses on determining the maximum velocity for the Poiseuille Equation, specifically for water flowing through pipes with diameters of 0.001m, 0.015m, and 0.20m, while also addressing the same scenario using air. The Poiseuille Equation, applicable only for laminar flow, indicates that the maximum velocity corresponds to the transition point from laminar to turbulent flow. Key factors include the fluid's viscosity, pipe diameter, and pressure drop per unit length, which must be calculated for each scenario to establish the maximum allowable velocity.

PREREQUISITES
  • Understanding of the Poiseuille Equation and its application to fluid dynamics
  • Knowledge of laminar and turbulent flow characteristics
  • Familiarity with fluid viscosity and its impact on flow rates
  • Basic principles of pressure drop in fluid systems
NEXT STEPS
  • Calculate the maximum velocity for water using the Hagen-Poiseuille law for each specified pipe diameter
  • Analyze the transition point from laminar to turbulent flow for air in the same pipe diameters
  • Explore the effects of varying fluid viscosities on flow characteristics
  • Investigate the Reynolds number and its role in determining flow regimes
USEFUL FOR

Students and professionals in mechanical engineering, fluid mechanics researchers, and anyone involved in the design and analysis of piping systems will benefit from this discussion.

simonre7
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The question is as follows:

Determine the maximum velocity at which the poiseuille Equation may be used for
a) water flowing in pipes diameter 0.001m, 0.015m & 0.20m, stating f, pressure drop/length in each case.
b) Re-work question a) using air instead of water.

I am a bit confused as to how i reach the maximum velocity in each lengths of pipe any help would be greatly appriciated guys.

thank you in advance.
 
Physics news on Phys.org
Think in terms of transition from laminar to turbulent flow - Poiseuille's law (or the Hagen-Poiseuille law) is valid for laminar flow. The maximum velocity is that velocity (or speed) where the flow begins transition from laminar to turbulent.
 

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