How come in these Bernoulli problems, the Pressures on both sides cancel?

Question

If you have an open tank filled with water, and you poke a hole half way down the tank, you can solve for things like the speed of the water coming out of the hole with the Bernoulli's equation, $P_1 + \rho gh + \frac{1}{2}\rho v_1^2=P_2 + \rho gh_2 + \frac{1}{2}\rho v_2^2$

Why do these pressures cancel out?

Answer 1

If the tank is open, the surface of the liquid inside is exposed to atmospheric pressure. Same for the liquid flowing out the hole in the side.