Question

Stoke's law states that the viscous drag force $F$ experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity $\eta$, is given by $F=6\pi \eta av$
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
$\frac{v}{t}=k{\left(\frac{p}{l}\right)}^a{\eta }^b{r}^c$
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. $a=1,b=-2,c=-4$

Answer 1

The correct option is A $a=1,b=-1,c=4$

$\frac{V}{t}={\left(\frac{p}{l}\right)}^a{\eta }^b{r}^c$
$L^3{T}^{-1}=\left(M{L}^{-2}{T}^{-2}{)}^a{L}^c\right(M{L}^{-1}{T}^{-1}{)}^b$
$a+b=0$
$-2a-b+c=3$
$-2a-b=-1$
$c=4,a=1,b=-1$
Ans (A) is correct.