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 ......... $\%$
Medium
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(b) $V = \frac{{P\pi {r^4}}}{{8\eta l}}$ ==> $\frac{{{V_2}}}{{{V_1}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4}$
==> ${V_2} = {V_1}{\left( {\frac{{110}}{{100}}} \right)^4}$$ = {V_1}{(1.1)^4} = 1.4641V$
$\frac{{\Delta V}}{V} = \frac{{{V_2} - {V_1}}}{V} = \frac{{1.4641V - V}}{V} = 0.46\;\;\;{\rm{or}}\;\;\;46\% $.
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