Need to find relation between flow rate of air (cfm), and pressure (psi) inside varying tube sizes.?

Question

I have a vacuum that moves 200cfm of air at a pressure of 1.842psi through a tube 1.5in. in diameter. I need to know how much air it will move and how much of a pressure drop will I have if I switched to a 4 or 6in. diameter tube.

Answer 1

This appears to be a laminar flow situation, governed by Poiseuille's Law. F = (∆P/∆X)*π*R^4/(8*k); from this equation the pressure drop ∆P will vary inversely as the fourth power of the tube diameter. The amount of air flow and pressure are directly related; so you either increase the pressure to make the same flow, or decrease the flow to keep the same pressure drop or anything in between.

Answer 2

Neither Bernoulli's equation or Poiseuille's Law are applicable here. Bernoulli is conservation of energy without frictional losses. Poiseuille requires laminar flow. Your flow is tubulent, not laminar and the frictional losses govern the flow rate. A few previous answers say the flow is laminar. Macroscale fluid flow is very seldom laminar. Laminar flow does not exist above Reynolds number of 20,000. Your Reynolds number is 200,000.

You need to use the Colebrook equation or its graphical equivalent, the Moody diagram. The Colebrook equation is an empirical relation specifically for turbulent flow in tubes. You can find lots of references to each on line. This website does the calculation for you:

http://www.lmnoeng.com/moody.htm

Answer 3

Bernoulli's Equation