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  4. A liquid flows through two capillary tubes connected in series. Their lengths are L and 2 L and radii r and 2 r respectively. Then the pressure differences across the first and the second tube are in the ratio

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Q. A liquid flows through two capillary tubes connected in series. Their lengths are $L$ and $2 L$ and radii $r$ and $2 r$ respectively. Then the pressure differences across the first and the second tube are in the ratio

Mechanical Properties of Fluids

Solution:

$ V=\frac{\pi P r^{4}}{8 \eta l}$
As tubes are in series
$V_{1}=V_{2} \Rightarrow \frac{P_{1} r_{1}^{4}}{l_{1}}=\frac{P_{2} r_{2}^{4}}{l_{2}} \Rightarrow \frac{P_{1}}{P_{2}}=\left(\frac{l_{1}}{l_{2}}\right)\left(\frac{r_{2}}{r_{1}}\right)^{4}$
$=\left(\frac{L}{2 L}\right)\left(\frac{2 r}{r}\right)^{4}=8$