The rate of steady volume flow of water throu | vedclass

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(B) According to Poiseuille's law,the rate of steady volume flow $V$ through a capillary tube is given by $V = \frac{\pi p r^4}{8 \eta l}$.This can be

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$\frac{V}{17}$

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(B) According to Poiseuille's law,the rate of steady volume flow $V$ through a capillary tube is given by $V = \frac{\pi p r^4}{8 \eta l}$.This can be rewritten as the pressure difference $p = V \left( \frac{8 \eta l}{\pi r^4} \right) = V R_H$,where $R_H = \frac{8 \eta l}{\pi r^4}$ is the hydraulic resistance.For the first tube,$R_1 = \frac{8 \eta l}{\pi r^4}$.For the second tube,$R_2 = \frac{8 \eta l}{\pi (r/2)^4} = \frac{8 \eta l}{\pi r^4 / 16} = 16 R_1$.In a series combination,the total pressure difference $p$ is the sum of pressure differences across each tube: $p = p_1 + p_2 = V' R_1 + V' R_2$,where $V'$ is the new rate of flow.Since $p = V R_1$,we have $V R_1 = V' (R_1 + 16 R_1) = V' (17 R_1)$.Therefore,$V = 17 V'$,which gives $V' = \frac{V}{17}$.

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