Q. Under a constant pressure head, the rate of flow of liquid through a capillary tube is $V$. If the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become
A) $V/4$
B) $16\ V$
C) $V/8$
D) $V/32$
Explanation
(d) Rate of flow under a constant pressure head,
$V = \frac{\pi pr^{4}}{8\eta l} \Rightarrow V \propto \frac{r^{4}}{l}\ \Rightarrow \frac{V_{2}}{V_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{4} \times \frac{l_{1}}{l_{2}} = \left( \frac{1}{2} \right)^{4} \times \frac{1}{2}$
$\Rightarrow V_{2} = \frac{V_{1}}{32} = \frac{V}{32}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.