When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.

The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the product of the pressure and the differential area. The pressure can also be expressed in terms of the specific weight of the fluid and the depth of the strip into the fluid.

To derive the resultant force acting on the plate, the force acting on each strip of the plate is integrated over the entire plate area.

The weighted average of the depths of all points on the plate is used to determine the centroid of the plate. The resultant force acting on the plate is equal to the area of the plate multiplied by the pressure at a depth of its centroid.

The line of action of the resultant force passes through the centroid of the volume under the pressure distribution and intersects the plate at the center of pressure. It is important to note that the centroid of the plate and the center of pressure do not always coincide. The centroid of the plate represents the geometric center of the plate, while the center of pressure represents the point on the plate where the resultant force acts.

The resultant force acting on the plate is equivalent to the weight of the volume of fluid displaced by the plate. This means that the resultant force can also be calculated as the volume under the pressure distribution.