Q 11-09-066JEE MainJEE Main 2024 (27 Jan, Shift 2)Easy
The reading of a pressure metre attached with a closed pipe is $4.5\times10^4\ \text{N m}^{-2}$. On opening the valve, water starts flowing and the reading of pressure metre falls to $2.0\times10^4\ \text{N m}^{-2}$. The velocity of water is found to be $\sqrt V\ \text{m s}^{-1}$. The value of $V$ is ______.
Numerical value type. Enter your answer.
Answer: 50
By Bernoulli's theorem, the drop in pressure appears as kinetic energy per unit volume:
$$\frac12\rho v^2 = (4.5 - 2.0)\times10^4 = 2.5\times10^4$$
$$v^2 = \frac{2\times2.5\times10^4}{1000} = 50 \;\Rightarrow\; V = 50$$
Solution by Sreeraj P, M.Sc Physics