Fluid Pressure over Flat Plate of Variable Width

When a flat plate of varying width is submerged in a fluid, the fluid exerts pressure on the plate.

The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate.

The magnitude of the force is equal to the product of the pressure and the differential area, where pressure is proportional to the depth of the strip in the fluid.

Substituting the pressure in the force equation and integrating it gives the resultant force.

Expressing the area integral in terms of the depth of the centroid of the plate gives the resultant force as the product of plate area and the pressure at its centroid. This is equivalent to the volume under the pressure distribution.

The line of action of the resultant force passes through the centroid of this volume and intersects the plate at the center of pressure.

In such cases, the centroid of the plate does not always coincide with the center of pressure of the plate.