I can not understand why the surface area that atmospheric pressure is acting upon does not matter when calculating pressure.
For example look at the water jug below with 2 openings, one small and one big.
The atmospheric pressure per cm2 is the same on both sides. However, since one hole has less surface area and the other has more surface area does that not mean that the total force being exerted on the bigger hole is bigger than the other? If that is the case, why does the water not shoot out of the smaller hole since the total force on the hole to the right is bigger?
I think my problem is that I am thinking of pressure in terms of weight, which is wrong perhaps. I imagine the above image as like a seesaw, where the right is heavier therefore the left should rise up but that is obviously not the case. Why is it not the case?
The same question worded differently would be: Why is the surface area of the mercury exposed to the air in a mercury barometer not taken into equation?