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, given that the rate of flow is proportional to the fourth power of the radius. Use k for the proportionality constant. R(r) =________--

(b) If R = 400 cm3/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. R(r) = ___________-

(c) What is the rate of flow of the same gas through a pipe of radius 3?

Answer 1

Answer:

a) R(r) = kr⁴

b) R(r) = 1.5625 r⁴

c) R = 126.56 cm³/s when r = 3 cm

Step-by-step explanation:

Rate of flow of a gas through a cylindrical pipe = R

radius of the pipe = r

a) R ∝r⁴

R(r) = kr⁴ where k is the proportionality constant.

R(r) means R is a function of r.

b) R(r) = kr⁴

R = 400 cm³/s, r = 4 cm

400 = k × 4⁴

k = 400/4⁴ = 400/256 = 1.5625 (cm.s)⁻¹

R(r) = 1.5625 r⁴

c) R(r) = 1.5625 r⁴

R = ?

r = 3 cm

R = 1.5625 × 3⁴ = 126.5625 cm³/s = 126.56 cm³/s