The rate of steady volume flow of water throu | vedclass

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(B) The rate of flow of water through a capillary tube is given by Poiseuille's equation: $V = \frac{\pi p r^4}{8 \eta l}$.This can be rewritten as a

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$\frac{V}{17}$

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(B) The rate of flow of water through a capillary tube is given by Poiseuille's equation: $V = \frac{\pi p r^4}{8 \eta l}$.This can be rewritten as a pressure drop: $p = V \left( \frac{8 \eta l}{\pi r^4} \right) = V R_h$, 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 drops: $p = p_1 + p_2 = V' R_1 + V' R_2$, where $V'$ is the new flow rate.Since $p = V R_1$, we have $V R_1 = V' (R_1 + 16 R_1) = V' (17 R_1)$.Therefore, $V' = \frac{V}{17}$.

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