The total pressure force on a plane area is equal to the area multiplied by the intensity of pressure at its centroid, if

ANS:D - all the above.

1. If the area is horizontal: In this case, the pressure at any point on the area would be the same since the depth of each point from the free surface of the fluid is identical. Therefore, the pressure at the centroid of the area represents the pressure throughout the entire area. As a result, the total pressure force on the horizontal area can be calculated by multiplying the area by the intensity of pressure at its centroid.
2. If the area is vertical: This scenario is the most straightforward case for calculating hydrostatic pressure. The pressure at any point on the vertical area varies linearly with depth due to hydrostatic pressure. The pressure at the centroid of the area represents the average pressure over the entire area. Thus, the total pressure force on the vertical area can be calculated by multiplying the area by the intensity of pressure at its centroid.
3. If the area is inclined: When the area is inclined, the pressure distribution varies across the surface. To calculate the total pressure force on the inclined area, you need to integrate the pressure over the entire area, taking into account the varying pressure at different points. This involves resolving the pressure into components normal and parallel to the plane of the area and integrating these components over the area.