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 P₁. The reading of the pressure gauge falls to P₂ when the valve is opened. The speed of water flowing in the pipe is proportional to (a) (P₁ - P₂)² (b) √(P₁ - P₂) (c) P₁ - P₂ (d) (P₁ - P₂)⁴

Answer: (b). Closed valve: v = 0, gauge reads P₁. Open valve: gauge reads P₂ with speed v. Bernoulli: P₁ - P₂ = 1/2ρ v² ⇒ v = √((2(P₁ - P₂))/(ρ)) So v ∝ √(P₁ - P₂), answer (b).

Water flows in a horizontal pipe whose one end is closed with a… | JEE Main 2025 (23 Jan, Shift 2)

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Bernoulli's Equation

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

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Answer: (b)

Closed valve: $v = 0$ , gauge reads $P_1$ . Open valve: gauge reads $P_2$ with speed $v$ .
Bernoulli: $P_1 - P_2 = \frac{1}{2}\rho v^2 \Rightarrow v = \sqrt{\dfrac{2(P_1 - P_2)}{\rho}}$
So $v \propto \sqrt{P_1 - P_2}$ , answer (b).

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