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.
