Q. A capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by 10% then the rate of flow of liquid will change nearly by
A) + 10%
B) + 46%
C) $- 10\%$
D) $- 40\%$
Explanation
(b) $V = \frac{P\pi r^{4}}{8\eta l} \Rightarrow \frac{V_{2}}{V_{1}} = \left( \frac{r_{2}}{r_{1}} \right)^{4}$
$\Rightarrow V_{2} = V_{1}\left( \frac{110}{100} \right)^{4} = V_{1}(1.1)^{4} = 1.4641V$
$\frac{\mathrm{\Delta}V}{V} = \frac{V_{2} - V_{1}}{V} = \frac{1.4641V - V}{V} = 0.46$ or 46%
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.