Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the…
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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
[JEE Main 2025, 23 Jan (Shift 2)]
✓ Correct answer: d)
\(\sqrt{{P}_{1}-{P}_{2}}\)
Explanation
\(\text{ Apply Bernoulli's eqn }\\ \frac{{P}_{1}}{\rho g}+\frac{{V}_{1}^{2}}{2g}=\frac{{P}_{2}}{\rho g}+\frac{{V}_{2}^{2}}{2g}\\ \frac{{P}_{1}}{\rho g}+0=\frac{{P}_{2}}{\rho g}+\frac{{V}^{2}}{2g}\\ V=\sqrt{\frac{2\left({P}_{1}-{P}_{2}\right)}{\rho }}\\ V\propto \sqrt{\left({P}_{1}-{P}_{2}\right)}\)
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