The rate of steady volume flow of water throu | vedclass

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(B) The rate of steady volume flow of a liquid through a capillary tube is given by Poiseuille's equation: $V = \frac{P}{R}$,where $R$ is the fluid re

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$\frac{V}{17}$

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(B) The rate of steady volume flow of a liquid through a capillary tube is given by Poiseuille's equation: $V = \frac{P}{R}$,where $R$ is the fluid resistance.Fluid resistance is defined as $R = \frac{8\eta l}{\pi r^4}$.For the first tube,$R = \frac{8\eta l}{\pi r^4}$.For the second tube of same length $l$ but radius $r' = \frac{r}{2}$,the resistance $R'$ is:$R' = \frac{8\eta l}{\pi (r/2)^4} = \frac{8\eta l}{\pi r^4} 	imes 16 = 16R$.When connected in series,the total resistance $R_{eq} = R + R' = R + 16R = 17R$.The new rate of flow $V_{new}$ under the same pressure difference $P$ is:$V_{new} = \frac{P}{R_{eq}} = \frac{P}{17R}$.Since $V = \frac{P}{R}$,we get $V_{new} = \frac{V}{17}$.

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