How to Determine Flow Rate in a Pipe Using Fluid Dynamics?

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SUMMARY

The discussion focuses on calculating the flow rate in a pipe using fluid dynamics principles, specifically Bernoulli's equation and the Hagen–Poiseuille equation. The user attempts to apply Bernoulli's equation but finds it ineffective due to equal diameters at both ends of the pipe, leading to the cancellation of terms. The user also considers the Hagen–Poiseuille equation but notes its limitation in accounting for the height of the pipe. The key takeaway is that while both equations are relevant, additional factors must be considered for accurate flow rate determination.

PREREQUISITES
  • Understanding of Bernoulli's equation
  • Familiarity with Hagen–Poiseuille equation
  • Knowledge of fluid dynamics concepts
  • Basic principles of pressure and flow in pipes
NEXT STEPS
  • Research the impact of pipe height on flow rate calculations
  • Learn about the continuity equation in fluid dynamics
  • Explore advanced fluid dynamics simulations using software like ANSYS Fluent
  • Investigate the effects of viscosity on flow rate in different fluids
USEFUL FOR

Students studying fluid dynamics, engineers working on pipe flow systems, and anyone involved in hydraulic design or analysis.

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Homework Statement


http://imgur.com/DSBFIeO
I want to find the flowrate through this pipe based on the pipe's diameter, height of the pipe and the pressure difference. I tried to use Bernoulli, but since the diameter on either end is the same, the terms cancel out. I guess Bernoulli's equation doesn't apply in this example

Homework Equations


https://en.wikipedia.org/wiki/Bernoulli's_principle
https://en.wikipedia.org/wiki/Hagen–Poiseuille_equation

The Attempt at a Solution


P_1 + \rho g h_1 + \dfrac{1}{2}\rho {v_1}^2 = P_2+ \rho g h_2 + \dfrac{1}{2}\rho {v_2}^2 \\<br /> {v_2}^2-{v_1}^2 = \dfrac{|P1-P2|-\rho g h_2}{0.5\rho}\\[2mm]<br />
I also looked at Poiseuille's equation: \dfrac{\Delta V}{\Delta t}=\dfrac{\pi r^4 (P_1-P_2)}{8\eta l},\\[2mm]
but this does not take the height of the pipe into effect.
 
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man the forums are dead now could you please take a look at my homework?
 

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