Forces On a Flat Surface

Finding the resultant force

The centroid of a surface is a single point through which lines can be drawn in any direction, and the areas on either side of the line would be the same. The location of the centroid is important for determining the second moment of area, and also for finding the average pressure.

The pressure exerted on the surface by the fluid at the centroid is the average of the pressure experienced over the whole surface. That is to say that, if the surface experienced a constant pressure all over of the same pressure as that at the centroid, the total force exerted on the surface would be the same.

Therefore, the simplest way to find the total force exerted on a submerged surface is to find the pressure at the centroid and multiply it by the total area.

Important Note

If you have a situation similar to that shown in the second diagram, where a fluid acts on one side of a surface and the atmosphere acts on the other, then you can use gauge pressure of the fluid and ignore the atmosphere on the other side.