Two tubes of radii r_1 and r_2,and lengths l_ | vedclass

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(D) For a liquid flowing through tubes in series under streamline conditions,the rate of flow of liquid $(V)$ remains constant through both tubes.Acco

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$\frac{r_1}{2}$

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(D) For a liquid flowing through tubes in series under streamline conditions,the rate of flow of liquid $(V)$ remains constant through both tubes.According to Poiseuille's equation,the rate of flow is given by $V = \frac{\pi P r^4}{8 \eta l}$.Since $V_1 = V_2$,we have:$\frac{\pi P_1 r_1^4}{8 \eta l_1} = \frac{\pi P_2 r_2^4}{8 \eta l_2}$Simplifying the expression,we get:$\frac{P_1 r_1^4}{l_1} = \frac{P_2 r_2^4}{l_2}$Given that $P_2 = 4P_1$ and $l_2 = \frac{l_1}{4}$,substitute these values into the equation:$\frac{P_1 r_1^4}{l_1} = \frac{(4P_1) r_2^4}{l_1 / 4}$$\frac{P_1 r_1^4}{l_1} = \frac{16 P_1 r_2^4}{l_1}$$r_1^4 = 16 r_2^4$Taking the fourth root on both sides:$r_1 = 2 r_2$Therefore,$r_2 = \frac{r_1}{2}$.

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