Q 11-09-127JEE MainJEE Main 2020 (6 Sep, Shift 2)Easy
A fluid is flowing through a horizontal pipe of varying cross-section, with speed $v\ \text{m s}^{-1}$ at a point where the pressure is $P$ pascal. At another point where the pressure is $\dfrac P2$ pascal, its speed is $V\ \text{m s}^{-1}$. If the density of the fluid is $\rho\ \text{kg m}^{-3}$ and the flow is streamline, then $V$ is equal to:
Answer: (D) $\sqrt{\dfrac P\rho + v^2}$
Bernoulli's equation for a horizontal pipe:
$$P + \frac12\rho v^2 = \frac P2 + \frac12\rho V^2$$
$$V^2 = v^2 + \frac P\rho \Rightarrow V = \sqrt{\frac P\rho + v^2}$$
Solution by Sreeraj P, M.Sc Physics