JEE Main 2025 Jan 23 Shift 2, Physics Q8: Hydrodynamic

JEE Main2025Jan 23, Shift 2Physics

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

Solution

Before opening the valve the water is at rest at the gauge location, with pressure $P_{1}$ . After opening, the gauge reads $P_{2}$ and the water flows with speed $v$ .

Apply Bernoulli's equation along a horizontal streamline from the static state to the moving state (same height, so the $ρ g h$ term cancels):

$P_{1} + 0 = P_{2} + \frac{1}{2} ρ v^{2} \Rightarrow v = \frac{2 ( P _{1} - P _{2} )}{ρ} .$

Hence $v \propto P_{1} - P_{2} .$

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JEE Main 2025 Jan 23 Shift 2, Physics Q8: Hydrodynamic

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