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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?

Respuesta :

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

abidemiokin
  • If the rate of flow is proportional to the fourth power of the radius, the expression will be [tex]R =kr^4[/tex]
  • A formula for the rate of flow of that gas through a pipe of radius "r" is[tex]R(r)=1.5625r^4[/tex]
  • The rate of flow of the same gas through a pipe of radius 3 is 126.5625cm³/s

Let the rate of flow of gas through the pipe be R

Let the radius of the pipe be "r"

a) If the rate of flow is proportional to the fourth power of the radius, this is expressed as:

[tex]R \ \alpha \ r^4[/tex]

Introducing the proportionality constant, the expression becomes;

[tex]R =kr^4[/tex]

b) Given the following parameters

R = 400 cm³/sec

r = 4cm

Substitute into the expression in (a)

[tex]400=4^4k\\400 =256k\\k=\frac{400}{256}\\k= 1.5625[/tex]

Substitute the proportionality constant into the original equation

[tex]R(r)=1.5625r^4[/tex]

This gives a formula for the rate of flow of that gas through a pipe of radius

c) Given that the radius is 3cm, the rate of flow of the gas through the pipe will be expressed as;

[tex]R(r)=1.5625(3)^4\\R(r)=1.5625(81)\\R(r) =126.5625cm^3/s[/tex]

Hence the rate of flow of the same gas through a pipe of radius 3 is 126.5625cm³/s

Learn more here: https://brainly.com/question/15545558

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