Poiseuille\'s Law gives the rate of flow, , of a gas through a cylindrical pipe
ID: 3215714 • Letter: P
Question
Poiseuille's Law gives the rate of flow,, of a gas through a cylindrical pipe in terms of the radius of the pipe,, for a fixed drop in pressure between the two ends of the pipe.(a)Find a formula for Poiseuille's Law, given that the rate of flow is proportional to the fourth power of the radius.
........
(Usekfor any constant of proportionality you may have in your equation.)
(b)Ifcm/s in a pipe of radius 3 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radiuscm.
..........cm/s
(c)What is the rate of flow of the same gas through a pipe with a 4 cm radius?
......cm/s
Explanation / Answer
a) Since this states that it is proportional to the fourth power of the radius, we have the following formula: R(r) = kr^4 b) Since R(r) = 400, and r = 4. We have: R(r) = kr^4 ==> 400 = k(4)^4 ==> 400 = 256k ==> k = 25/16 So the equation is R(r) = (25/16)r^4. c) Using the equation from b, we can get the rate of flow. Doing so yields: R(r) = (25/16)3^4 ==> R(r) = (25/16)(81) ==> R(r) = 2025/16 Therefore, the rate of flow is 2025/16 cm^3/sec. I hope that helps!