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Stoke's law states that the viscous drag...

Stoke's law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity `eta`, is given by `F=6 pi eta` If this fluid is flowing through a cylindrical pipe of radius r, length `l` and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as
`(V)/(t)=K ((p)/(l))^(a)eta^(b)r^(c )`
where k is a dimensionless constant. Correct values of a, b and c are -

A

`a=1, b=-1, c=4`

B

`a=-1, b=1, c=4`

C

`a=2, b=-1, c=3`

D

`a=1, b=-2, c=-4`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Stoke’s law states that the viscous drag force F experienced by a sphere of radius a, moving with a speed V through a fluid with coefficient of viscosity eta , is given by F = 6pi"na"v . If this fluid is flowing through a cylindrical pipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as c (V)/(t)=k((P)/(l))eta^(b)r^(c) , where k is a dimensional constant. Correct values of a, b and c are

    A
    a = 1, b = –1, c = 4
    B
    a = `–1`, b = 1, c = 4
    C
    a = 2, b =` –1`, c = 3
    D
    a = 1, b =` –2, c = –4`

  • Viscous force on a small sphere of radius r moving in a fluid varies directly with

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    `r^(2)`
    B
    r
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    `1/r`
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    `((1)/(r ))^(2)`

  • A liquid of coefficient of viscosity eta is flowing steadily through a capillary tube of radius r and length I. If V is volume of liquid flowing per sec. the pressure difference P at the end of tube is given by

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    `P =(8piIV)/(eta r^4)`
    B
    `P = (8eta r^4 I)/(piV)`
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    `P = (8etaIV)/(pir^4)`
    D
    `P =(8eta r^4 V)/(pi I)`

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