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(B) According to Poiseuille's law,the rate of flow of liquid $V$ through a capillary tube is given by: $V = \frac{P \pi r^4}{8 \eta l}$ Since $P$,$\et

Vedclass · Accepted Answer

$46$

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(B) According to Poiseuille's law,the rate of flow of liquid $V$ through a capillary tube is given by: $V = \frac{P \pi r^4}{8 \eta l}$ Since $P$,$\eta$,and $l$ are constant,we have $V \propto r^4$. If the radius $r$ is increased by $10\%$,the new radius $r_2 = 1.1 r_1$. The new rate of flow $V_2$ is given by: $V_2 = V_1 \left( \frac{r_2}{r_1} ight)^4 = V_1 (1.1)^4 = 1.4641 V_1$. The percentage change in the rate of flow is: $\frac{\Delta V}{V_1} 	imes 100 = \frac{V_2 - V_1}{V_1} 	imes 100 = (1.4641 - 1) 	imes 100 = 46.41\% \approx 46\%$. Thus,the rate of flow increases by approximately $46\%$.

$A$ 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 ......... $\%$

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