Question

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. -0.1
• D. -0.4

Answer 1

Answer: (B)

46%

Answer 2

Volume o liquid flowing through capillary per second is given by $V=\frac{\pi p{{r}^{4}}}{8\eta l}$ $\therefore$ $V\propto {{r}^{4}}$ $\Rightarrow$ $\frac{{{V}_{2}}}{{{V}_{1}}}={{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{4}}$ $\therefore$ ${{V}_{2}}={{V}_{1}}{{\left( \frac{110}{100} \right)}^{4}}={{V}_{1}}{{(1.1)}^{4}}$ $=1.4641\,V$ $\therefore$ $\frac{\Delta V}{V}=\frac{{{V}_{2}}-{{V}_{1}}}{V}$ $=\frac{1.4641\,V-V}{V}$ $=0.46$ or $46$%