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. $16\, V$
• C. $ \frac{V}{8} $
• D. $ \frac{V}{32} $

Answer 1

Answer: (D)

Rate of flow under a constant pressure head
$V=\frac{\pi p r^{4}}{8 \eta l}$
$\Rightarrow V \propto \frac{r^{4}}{l}$
$\Rightarrow \frac{V_{2}}{V_{1}}=\left[\frac{r_{2}}{r_{1}}\right]^{4} \times \frac{l_{1}}{l_{2}}$
$=\left[\frac{1}{2}\right]^{4} \times \frac{1}{2}$
$\Rightarrow V_{2}=\frac{V_{1}}{32}=\frac{V}{32}$