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
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]
- A
$\sqrt{\frac{ P }{2 \rho}+ v ^{2}}$
- B
$\sqrt{\frac{ P }{\rho}+ v ^{2}}$
- C
$\sqrt{\frac{2 P }{\rho}+ v ^{2}}$
- D
$\sqrt{\frac{ P }{\rho}+ v }$
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- [JEE MAIN 2022]
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