A dimensionally consistent relation for the volume ' V ' of a liquid of coefficient of viscosity η flowing per second through a tube of radius ' r' and length ' ℓ ' having a pressure ' P ' across its ends, is

Question

A dimensionally consistent relation for the volume ' V ' of a liquid of coefficient of viscosity η flowing per second through a tube of radius ' r' and length ' ℓ ' having a pressure ' P ' across its ends, is (A) v =(π Pr 4/8 η ℓ) (B) v =(π η ℓ/8 Pr 4) (C) v =(8 P η ℓ/π r 4) (D) v =(π P η/8 ℓ r 4)

Tardigrade Admin · Accepted Answer

V=(π Pr4/8 η l) = Rate of flow

Q. A dimensionally consistent relation for the volume ' $V$ ' of a liquid of coefficient of viscosity $η$ flowing per second through a tube of radius ' $r$ ' and length ' $ℓ$ ' having a pressure ' $P$ ' across its ends, is

$v = \frac{π P r ^{4}}{8 η ℓ}$

$v = \frac{π η ℓ}{8 P r ^{4}}$

$v = \frac{8 P η ℓ}{π r ^{4}}$

$v = \frac{π P η}{8 ℓ r ^{4}}$

$V = \frac{π P r ^{4}}{8 η l}$
$=$ Rate of flow

Q. A dimensionally consistent relation for the volume ' V ' of a liquid of coefficient of viscosity η flowing per second through a tube of radius ' r' and length ' ℓ ' having a pressure ' P ' across its ends, is

v=8ηℓπPr4​

v=8Pr4πηℓ​

v=πr48Pηℓ​

v=8ℓr4πPη​