Question

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

• A. Four times that of $Q$
• B. Two times that of $Q$
• C. $\frac{1}{2}$ times that of $Q$
• D. $\frac{1}{4}$ times that of $Q$

Answer 1

Answer: (A)

Rate of flow through both pipes will be same
i.e., $Q_1=Q_2$
$\frac{V_1}{t}=\frac{V_2}{t}$
$\frac{\pi r_1^2{l}_1}{t}=\frac{\pi r_2^2{I}_2}{t}$
$\left(\text{ Where }\frac{I_1}{t}=V_P\text{ and }\frac{l_2}{t}=V_Q\right)$
$\Rightarrow \frac{\pi d_1^2}{4}{V}_P=\frac{\pi d_2^2}{4}\times V_Q$
$\Rightarrow V_P={\left(\frac{d_2}{d_1}\right)}^2{V}_Q$
$\Rightarrow V_P={\left(\frac{4\times 10^{-2}}{2\times 10^{-2}}\right)}^2{V}_Q$
$\Rightarrow V_P=4V_Q$