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, given that the rate of flow is proportional to the fourth power of the radius. Use K as the constant of proportionality.
(b) If R= 500 cm^3/sec in a pipe of radius 4 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius r cm. Enter the exact answer.
(c) What is the rate of flow of the gas in part (b) through a pipe with a 5 cm radius?

a) R = Kr⁴

b) R = (500/256) r⁴ = (125/64) r⁴ = 1.953125 r⁴

c) R = 1220.7 cm³/s

Step-by-step explanation:

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) R ∝ r⁴

R = Kr⁴

Note that all the other parameters that are constant like the fixed pressure drop between the ends of the pipe are all represented by the constant of proportionality, K.

b) If R= 500 cm^3/sec in a pipe of radius 4 cm for a certain gas, find a formula for the rate of flow of that gas through a pipe of radius r cm. Enter the exact answer.

R = Kr⁴

R = 500 cm³/s

r = 4 cm

500 = K × 4⁴

K = (500/256)

K = 1.953125

R = Kr⁴ becomes

R = 1.953125 r⁴

c) The rate of flow of the gas in part (b) through a pipe with a 5 cm radius.

R = 1.953125 r⁴

r = 5 cm

R = 1.953125 (5⁴)

R = 1,220.703125 = 1220.7 cm³/s

Hope this Helps!!!

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step-by-step explanation:

the most boring thing ever written

step-by-step explanation:

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