Poiseuille\'s Law gives the rate of flow, R, of a gas through a cylindrical pipe

Question

Poiseuille's Law gives the rate of flow, R, of a gas through a cylindrical pipe in terms of the radius of the pipe, r, for a fixed drop in pressure between the two ends of the pipe. a) Find a formula for Poiseuille's Law by using k as the proportional constant value, given that the rate of flow is proportional to the fourth power of the radius. Ra where k is a constant. (b) If R-500 cm2/sec 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 radius r cm. Round your answer to three decimal places, if necessary R: e) What is the rate of flow of the same gas through a pipe with a 5 em radius? Round your answer to two decimal places. R: cm/sec

Explanation / Answer

(a) Since , the flow rate R is proportional to the fourth power of the radius with constant of proportionality as k , we can say the relation holds as below

R = kr4

(b) If R = 500 and r = 3 , then by plugging these values we can get the value of k

=> 500 = k(3)4

=> k = 500/81

(c) Calculating R when r = 5

R = (500/81)(5)4

=> R = 3858.0247

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