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., $Q_{1}=Q_{2}$
$\frac{V_{1}}{t}=\frac{V_{2}}{t}$
$\frac{\pi r_{1}^{2} l_{1}}{t}=\frac{\pi r_{2}^{2} I_{2}}{t}$
$\left(\text { Where } \frac{I_{1}}{t}=V_{P} \text { and } \frac{l_{2}}{t}=V_{Q}\right)$
$\Rightarrow \frac{\pi d_{1}^{2}}{4} V_{P}=\frac{\pi d_{2}^{2}}{4} \times V_{Q}$
$\Rightarrow V_{P}=\left(\frac{d_{2}}{d_{1}}\right)^{2} V_{Q}$
$\Rightarrow V_{P}=\left(\frac{4 \times 10^{-2}}{2 \times 10^{-2}}\right)^{2} V_{Q}$
$\Rightarrow V_{P}=4 V_{Q}$