Question

A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference P. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is

• A. (a) P
• A. (b) $rac{3P}{4}$
• A. (c) $rac{P}{2}$
• A. (d) $rac{P}{4}$

Answer 1

(d)

From $V = \frac{P\pi r^{4}}{8\eta l}$

⇒ $P = \frac{V8\eta l}{\pi r^{4}}$

⇒ $\frac{P_{2}}{P_{1}} = \frac{V_{2}}{V_{1}} \times \frac{l_{2}}{l_{1}} \times \left( \frac{r_{1}}{r_{2}} \right)^{4} = 2 \times 2 \times \left( \frac{1}{2} \right)^{4} = \frac{1}{4}$

⇒ $P_{2} = \frac{P_{1}}{4} = \frac{P}{4}$.