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

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