How do you find the total force of water pressing on a curved surface that's underwater?

To find the total force of water pressing on a curved surface that is underwater, we break down the complex force distribution into its horizontal and vertical components. This method simplifies the problem by converting it into calculations involving flat projected areas and volumes of water. Each component is determined separately, and then they are combined to find the resultant total force. The horizontal component of the force, often denoted as `F_x`, is equivalent to the hydrostatic force exerted on the vertical projection of the curved surface. The vertical projection is the area that would be created if the curved surface were projected onto a vertical plane, like a shadow cast by horizontal light. To calculate `F_x`, you find the pressure at the centroid of this vertical projected area and multiply it by the magnitude of the projected area. The centroid is the geometric center of an are....