The correct answer is D. all of the above.
The total pressure force on a plane area is equal to the area multiplied by the intensity of pressure at the centroid, regardless of the orientation of the area. This is because the intensity of pressure is a measure of the force per unit area, and the centroid is the point at which the entire area can be considered to act.
To understand this, consider a simple example of a rectangular area with a uniform pressure applied to its surface. The intensity of pressure at any point on the surface is equal to the pressure divided by the area of the rectangle. The total pressure force on the rectangle is then equal to the area of the rectangle multiplied by the intensity of pressure.
The centroid of the rectangle is located at its center, and the total pressure force on the rectangle can be calculated by multiplying the area of the rectangle by the intensity of pressure at the centroid. This is true regardless of the orientation of the rectangle.
For example, if the rectangle is horizontal, the total pressure force will be equal to the area of the rectangle multiplied by the intensity of pressure at the centroid. If the rectangle is vertical, the total pressure force will still be equal to the area of the rectangle multiplied by the intensity of pressure at the centroid. And if the rectangle is inclined, the total pressure force will still be equal to the area of the rectangle multiplied by the intensity of pressure at the centroid.
In conclusion, the total pressure force on a plane area is equal to the area multiplied by the intensity of pressure at the centroid, regardless of the orientation of the area.