Question

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. \( \sqrt{P_1 - P_2} \)
• B. \( (P_1 - P_2)^2 \)
• C. \( (P_1 - P_2)^4 \)
• D. \( P_1 - P_2 \)

Hint:

For fluids in motion, Bernoulli's equation relates the pressure difference to the speed of the fluid, often expressed as \( v \propto \sqrt{P_1 - P_2} \).

Answer 1

The Correct Option is A

From Bernoulli's equation, the velocity \( v \) of the fluid is related to the pressure difference \( P_1 - P_2 \) by: \[ v = \sqrt{\frac{2(P_1 - P_2)}{\rho}}, \] where \( \rho \) is the density of the fluid. Thus, the speed of water is proportional to: \[ \sqrt{P_1 - P_2}. \]