So again, simplifying this equation,

we get ps + 1/2 gamma delta z = pz.

But now, as I shrink this element down to a point,

down to zero, delta z turns to zero, so that terms goes out.

So, we get the very simple result again, that ps is equal to pz.

So, putting this together, we get that ps = py = pz = ps,

which brings us with the very important conclusion, that the pressure

acts equally in all directions at a point in a stationary fluid.

And this is sometimes called Pascal's law.

You can also show, but I won't show here,

that this also applies to a flowing fluid if there are no shear stresses acting.

The second major question that we want to address is,

how does pressure vary with position?

In order words, both with height and with horizontal position.