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

  $\left(\mathrm{P}_1-\mathrm{P}_2\right)^2$
• Correct answer
  D

  $\sqrt{\mathrm{P}_1-\mathrm{P}_2}$

Solution

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

Hence, the correct answer is option: 'D'.