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

[lurifax1]

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.

 

[vinamas]

man the forums are dead now could you please take a look at my homework?