Two water pipes $P$ and $Q$ having diameter $2 \times 10^{-2} \,m$ and $4 \times 10^{-2} \,m$ respectively are joined in series with the main supply line of water. The velocity of water flowing in pipe $P$ is ........
Medium
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(a)
Rate of flow through both pipes will be same
$\text { i.e., } Q_1=Q_2$
$\frac{V_1}{t}=\frac{V_2}{t}$
$\frac{\pi r_1^2 l_1}{t}=\frac{\pi r_2^2 l_2}{t}$
$\left(\text { Where } \frac{l_1}{t}=V_P \text { and } \frac{l_2}{t}=V_Q\right)$
$\Rightarrow \frac{\pi d_1^2}{4} V_P=\frac{\pi d_2^2}{4} \times V_Q$
$\Rightarrow V_P=\left(\frac{d_2}{d_1}\right)^2 V_Q$
$\Rightarrow V_P=\left(\frac{4 \times 10^{-2}}{2 \times 10^{-2}}\right)^2 V_Q$
$V_P=4 V_Q$
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