Question

Under a constant pressure head, the rate of flow of liquid through a capillary tube is $V$. If the length of the capillary tube is doubled and the diameter of the bore is halved, the rate of flow would become

• A. $\frac{V}{4}$
• B. $16V$
• C. $\frac{V}{8}$
• D. $\frac{V}{32}$

Answer 1

Answer: (D)

Rate of flow under a constant pressure head
$V=\frac{\pi p{r}^4}{8\eta l}$
$\Rightarrow V\propto \frac{r^4}{l}$
$\Rightarrow \frac{V_2}{V_1}={\left[\frac{r_2}{r_1}\right]}^4\times \frac{l_1}{l_2}$
$={\left[\frac{1}{2}\right]}^4\times \frac{1}{2}$
$\Rightarrow V_2=\frac{V_1}{32}=\frac{V}{32}$