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

The Correct Option is B

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$%