# Pressure in speed of efflux

While describing speed of efflux, using Bernoulli equation, we use value of $$P$$ at both openings as atmospheric pressure. Why don't we use $$P_\text{atmosphere}+\rho gh$$ for $$P$$ at bottom opening?

While writing Bernoulli's equation you write the equation for fluid just inside and just outside the container this leads to the fact that just outside pressure is equal to $$P_{atm}$$ and just inside it is $$P_{atm}+ \rho gh$$ . Note that the $$P_{atm}$$ term cuts off from both sides so you don't feel it's presence.
The pressure inside the tank is not $$P_{atm}+\rho g h$$ over the entire bottom of the tank. Within the tank, there is a disturbance in the pressure distribution in close proximity to the exit hole. The fluid flow is converging toward the exit hole, and, as it does, its velocity is building up; and its pressure is correspondingly decreasing. This all takes place within a distance of a few hole diameters approaching the exit hole (in all directions). At the very exit hole, the velocity reaches the exit velocity and the pressure reaches the atmospheric pressure.