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$\sqrt{\frac{ P }{2 \rho}+ v ^{2}}$
  • B$\sqrt{\frac{ P }{\rho}+ v ^{2}}$
  • C$\sqrt{\frac{2 P }{\rho}+ v ^{2}}$
  • D$\sqrt{\frac{ P }{\rho}+ v }$
JEE MAIN 2020, Medium
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