$A$ fluid is flowing through a horizontal pipe of varying cross-section,with speed $v \ m/s$ at a point where the pressure is $P \ Pa$. At another point where pressure is $\frac{P}{2} \ Pa$,its speed is $V \ m/s$. 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
  $\sqrt{\frac{2P}{\rho} + v^2}$
• D
  $\sqrt{\frac{P}{\rho} + v}$