Question 50 of 192

Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is $P_1$. The reading of the pressure gauge falls to $P_2$ when the valve is opened. The speed of water flowing in the pipe is proportional to

A$P_1-P_2$B$\left(P_1-P_2\right)^4$C$\left(\mathrm{P}_1-\mathrm{P}_2\right)^2$D$\sqrt{\mathrm{P}_1-\mathrm{P}_2}$

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Answer: (D) $\sqrt{\mathrm{P}_1-\mathrm{P}_2}$

Using Bernoulli's theorem
$\begin{aligned}
& P_1-P_2=\frac{1}{2} \rho v^2 \\
& v \propto \sqrt{P_1-P_2}
\end{aligned}$