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 are doubled is:

• A. $P$
• B. $\frac{3P}{4}$
• C. $\frac{P}{2}$
• D. $\frac{P}{4}$

Answer 1

Answer: (D)

$\frac{P}{4}$

$Q_{intial}=\frac{\pi P{r}^4}{8\eta L}$

$Q_{final}=2Q_{initial}=\frac{\pi 4P_1(r{)}^4}{8\eta L}$

$\Rightarrow P_1=\frac{P}{4}$