A fluid is flowing through a horizontal pipe of varying cross-section, with speed $v\;ms^{-1}$ at a point where the pressure is $P$ Pascal. At another point where pressure is $\frac{ P }{2}$ Pascal its speed is $V\;ms^{-1}$. If the density of the fluid is $\rho\, kg\, m ^{-3}$ and the flow is streamline, then $V$ is equal to
JEE MAIN 2020, Medium
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Applying Bernoulli's Equation
$P _{1}+\frac{1}{2} \rho v _{1}^{2}+\rho gy _{1}= P _{2}+\frac{1}{2} \rho v _{2}^{2}+\rho gy _{2}$
$P +\frac{1}{2} \rho v ^{2}=\frac{ P }{2}+\frac{1}{2} \rho V ^{2}$
$\frac{2 P }{2 \rho}+\frac{1}{2} \frac{\rho v ^{2}}{\rho} \times 2= V ^{2}$
$\sqrt{\frac{P}{\rho}+v^{2}}=V$
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