Pressure in a static fluid does not change in the horizontal direction as the horizontal forces balance each other out. However, pressure in a static fluid does change with depth, due to the extra weight of fluid on top of a layer as we move downwards.

Consider a column of fluid of arbitrary cross section of area, A:

Considering the weight of the column of water, we have:

Summary

1. Pressure acts normal to any surface in a static fluid;

2. Pressure is the same at a point in a fluid and acts in all directions;

3. Pressure varies linearly with depth in a fluid.

By applying these rules to a simple swimming pool, the pressure distribution around the edges is as shown:

Note:

1. Along the bottom the pressure is constant due to a constant depth;

2. Along the vertical wall the pressure varies linearly with depth and acts in the horizontal direction;

3. Along the sloped wall the pressure again varies linearly with depth but also acts normal to the surface;

4. At the junctions of the walls and the bottom the pressure is the same.