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Can I use Poiseuille's equation?

Also If I have a vacuum pump which says that its performance is 30 cubic feet per minutes and I have two pipes (one is radius R1 and L1, the other one is 2*R1 and 0.5*L1), will the vacuum do the same 30 CFM?

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1 Answer 1

As a fluid flows through a pipe it follows the law of continuity which states that Q = A1 V1 = A2 V2 = constant, where Q is the flow rate (cfm), A is the area of the pipe (ft^2) and V is the velocity of the fluid in the pipe (fpm). So whatever you make up in area you lose in velocity and vise versa since Q is constant (30 cfm).

In your experiment here, regarding condition 1 you could substitute in the continuity equation by R1 (Area = 3.14*R^2), you will find your corresponding velocity. In condition 2 that velocity will be a quarter of condition one's velocity value, and so on. Note: the length is irrelevant.

However you must consider one thing. If you reduced the radius to a point when velocity is large enough to make significant noise, which means loss of energy due to friction that could affect the flow rate. So in most possiblities your 30 cfm will not get affected.

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Your answer is assumed friction-less system and assume for a long flow. My case is a small volume. Please help. Thanks – Marco Apr 10 '13 at 5:52
@Marco What you asked about is what will happen if you switched pipes. If you switched pipes the flow rate wont get affected by this act alone. Actually the equation of continuity is a derivation from Bernoulli's principle in which friction is not a factor's_principle – Force Apr 10 '13 at 6:14
@Marco Is your pipes made from the same material? – Force Apr 10 '13 at 6:30
Thanks for your reply. I am asking about "Poiseuille's equation" NOT "Bernoulli's_principle" – Marco Apr 10 '13 at 6:41
I want to know whether I can use dV/dt equation (mass flow rate of Poiseuille equation in my case) – Marco Apr 10 '13 at 6:43

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