JEE Mains · Physics · STD 11 - 9.1 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 \(P_1-P_2\)
- B \(\left(P_1-P_2\right)^4\)
- C \(\left(\mathrm{P}_1-\mathrm{P}_2\right)^2\)
- D \(\sqrt{\mathrm{P}_1-\mathrm{P}_2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{\mathrm{P}_1-\mathrm{P}_2}\)
Step-by-step Solution
Detailed explanation
Using Bernoulli's theorem \(\begin{aligned} & P_1-P_2=\frac{1}{2} \rho v^2 \\ & v \propto \sqrt{P_1-P_2} \end{aligned}\)
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