Q 11-09-046JEE MainJEE Main 2025 (23 Jan, Shift 2)Easy
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
Answer: (D) $\sqrt{P_1 - P_2}$
Bernoulli's equation for the horizontal pipe, between the still water (valve closed) and the flowing water:
$$P_1 = P_2 + \frac{1}{2}\rho v^2 \Rightarrow v = \sqrt{\frac{2(P_1 - P_2)}{\rho}}$$
So $v \propto \sqrt{P_1 - P_2}$.
Solution by Sreeraj P, M.Sc Physics