Q. 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) $(P_1-P_2)^4$
C) $(P_1-P_2)^2$
D) $\sqrt{P_1-P_2}$
Explanation
[Solution by Dr. Abubacker] Bernoulli's equation for a horizontal pipe: $P_1=P_2+\frac12\rho v^2$, so $v=\sqrt{\frac{2(P_1-P_2)}\rho}\propto\sqrt{P_1-P_2}$. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.