Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge…

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
  1. $P_1-P_2$
  2. $\left(P_1-P_2\right)^4$
  3. $\left(\mathrm{P}_1-\mathrm{P}_2\right)^2$
  4. $\sqrt{\mathrm{P}_1-\mathrm{P}_2}$

Solution


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

Asked in: JEE Main 2025 (23 Jan Shift 2)

Practice more Mechanical Properties of Fluids questions on Aicharya