A closed pipe containing a liquid showed a pressure P₁ by gauge. When the valve was opened, pressure was reduced to P₂. The speed of water flowing out of the pipe is ( ρ = density of water) (a) [(4(P₁ - P₂))/(ρ)]1/2 (b) [(4(P₂ - P₁))/(ρ)]1/2 (c) [(2(P₁ - P₂))/(ρ)]1/2 (d) [(2(P₂ - P₁))/(ρ)]1/2

Answer: (c). Closed valve: v = 0, pressure P₁. Open valve: pressure P₂, speed v. Bernoulli: P₁ - P₂ = 1/2ρ v² v = [(2(P₁ - P₂))/(ρ)]1/2 So the answer is (c).

A closed pipe containing a liquid showed a pressure P₁ by gauge. When… | MHT CET 2024 (10 May, Shift 1)

Q11MHT CET 2024 · 10 MAY · SHIFT 1Medium

Bernoulli's Equation

A closed pipe containing a liquid showed a pressure $P_1$ by gauge. When the valve was opened, pressure was reduced to $P_2$ . The speed of water flowing out of the pipe is ( $\rho =$ density of water)

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Answer: (c)

Closed valve: $v = 0$ , pressure $P_1$ . Open valve: pressure $P_2$ , speed $v$ .
Bernoulli: $P_1 - P_2 = \frac{1}{2}\rho v^2$
$v = \left[\dfrac{2(P_1 - P_2)}{\rho}\right]^{1/2}$
So the answer is (c).

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Bernoulli's Equation question from MHT CET 2024 (10 May, Shift 1)

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