 In determining the forces acting on a submerged body, we are concerned with two things. First, the magnitude of the resulting hydrostatic force, and two, where that force is acting. The force of the applied fluid pressure is the pressure multiplied by the area of effect, but remember that the pressure changes as a function of height. For example, if we were to consider a very simple case, where, say, a one meter square is holding back a pool of water that perfectly touches the top of that square, you could say the gauge pressure at the top of the fluid is zero. Why am I talking about gauge pressure? Well, because atmospheric pressure in this hypothetical is acting on both sides of the gate. It's the pressure difference that we are concerned about. So the pressure, the gauge pressure, at the top would be zero and would linearly increase with height. The result is a triangle. Therefore, I know the force exerted by this pressure is going to be positioned a third of the way up the square. That's the point at which half the triangle is below my vector and half the triangle is above my vector. Therefore, I could say the fluid pressure is applied at a position two-thirds of a meter below the surface. Note that that is not the center of gravity of the square. The same logic applies to arbitrary shapes at arbitrary positions and arbitrary angles. The pressure increases with depth and we have to integrate to determine where the center of that applied fluid pressure appears. When you integrate the force term multiplied by position with respect to the surface, you end up with a function of the area moment of inertia of the shape. Also, since the face of the body is not necessarily perpendicular to the surface of the fluid, we have to multiply by the sign of the angle between the body and the surface so that our moment of inertia is described in the same reference frame as the pressure's function of depth. To make the math easier, we describe two dimensions, the distance between the centroid of the body and the center of applied hydrostatic force in the x-direction, and the distance between the centroid and the force in the y-direction. In this diagram, the center of applied force, that is abbreviated Cp, is offset from CG and we would describe this distance in the x-direction and this distance in the y-direction. And we would call them yCp and xCp. Therefore, we describe first the magnitude of the force applied by the fluid pressure by taking the specific weight of the fluid multiplied by the height from the fluid surface to the center of gravity of the face multiplied by area. Note that this is just the gauge pressure we know and love because specific weight is density of the fluid multiplied by gravity and then we multiply by height, that's the PAH equation, multiplied by area, so pressure multiplied by area is force, then we calculate the offset position of the center of applied force from the centroid of the shape. Note that the yCp parameter is defined in the up direction, that is towards the fluid's surface. If you get a negative number, that means the center of pressure is below the center of gravity. For example, if we got a yCp value that was positive and an xCp value of zero, that means our center of applied pressure is directly above our center of gravity. What is much more likely to happen, though, is that we will have a negative center of pressure. Therefore, our applied pressure will be below our center of gravity. That's why we have this negative term out front. The positive or negative value of these two terms is important. I think it will make more sense if we try an example.