# How to consider the pressure and the potential energy when use Bernoulli principle?

Suppose a situation where we are going to apply Bernoulli principle to find the velocity of a water stream leaving at the bottom of a large lake. When we apply the Bernoulli theory, we consider a stream line from the surface of the lake that runs through a hole located at the bottom of the dam, through which water is leaking. We consider a streamline and take the

pressure at the surface=atmospheric pressure

on the same streamline at the bottom, but inside the dam;

pressure =atmospheric pressure + hydrostatic pressure

so in this case the potential energy component at the top of the streamline has become the hydrostatic pressure component at the bottom of the streamline. in such a case should we neglect both hydrostatic pressure as well as potential energy component as they are going to be cancelled out?

$p_{atm}=p_{exit}-\rho g h+\frac{1}{2}\rho v^2$
Now $p_{exit}=\rho g h$ only if fluid is static, i.e. if there is no flow. If there is flow then $p_{exit}$ is unknown, as is $v$, so the equation is not much help unless you make some other assumption. If flow through the hole is discharging into atmosphere, then you may take $p_{exit}=p_{atm}$, and thus you get the familiar $v=\sqrt{2gh}$ formula.