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 $\mathrm{P}_{1}$. The reading of the pressure gauge falls to $\mathrm{P}_{2}$ when the valve is opened. The speed of water flowing in the pipe is proportional to

(A) $\sqrt{\mathrm{P}_{1}-\mathrm{P}_{2}}$

(B) $(\mathrm{P}_{1}-\mathrm{P}_{2})^{2}$

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Fluid Mechanics

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) $P_{1} - P_{2}$ ✓ Correct
(B) $(P_{1} - P_{2})^{2}$
(C) $(P_{1} - P_{2})^{4}$
(D) $P_{1} - P_{2}$

Answer: (A)

Solution

Applying Bernoulli's equation to the horizontal pipe — water at rest (

v = 0

) with the valve closed, moving with speed

v

once opened:

P_{1} = P_{2} + \frac{1}{2} ρ v^{2}

v = \frac{2 ( P _{1} - P _{2} )}{ρ}

The speed of the flowing water is proportional to

P_{1} - P_{2}

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option

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