A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is P/2 Pascal its speed is V ms–1. If the density of the fluid is ρ kg m–3 and the flow is streamline, then V is equal to: (a) √((P)/(2ρ) + v²) (b) √(P/ρ + v²) (c) √((2P)/(ρ) + v²) (d) √(P/ρ + v)

Answer: (b). Bernoulli (horizontal): P + 1/2ρ v² = P/2 + 1/2ρ V² P/2 = 1/2ρ(V² - v²) ⇒ V² = P/ρ + v² So the answer is (b) √(P/ρ + v²).

A fluid is flowing through a horizontal pipe of varying… | JEE Main 2020 (6 Sep, Shift 2)

Q23JEE Main 2020 · 6 SEP · SHIFT 2Medium

Bernoulli's Equation

A fluid is flowing through a horizontal pipe of varying cross-section, with

speed v ms–1 at a point where the pressure is P pascal. At another point where pressure is $\frac{P}{2}$ Pascal its speed is V ms–1. If the density of the fluid is $\rho$ kg m–3 and the flow is streamline, then V is equal to:

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Answer: (b)

Bernoulli (horizontal): $P + \frac{1}{2}\rho v^2 = \dfrac{P}{2} + \frac{1}{2}\rho V^2$
$\dfrac{P}{2} = \frac{1}{2}\rho(V^2 - v^2) \Rightarrow V^2 = \dfrac{P}{\rho} + v^2$
So the answer is (b) $\sqrt{\dfrac{P}{\rho} + v^2}$ .

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Bernoulli's Equation question from JEE Main 2020 (6 Sep, Shift 2)

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