Force on a plane wall
The gauge pressure in a liquid grows with depth: p = ρ·g·h. The total force on a plane wall of area A is F = ρ·g·h_C·A, where h_C is the depth of the centroid of the wall. The force acts along the normal to the wall. The pressure diagram on a vertical wall is a triangle (or a trapezoid if the upper edge is submerged), and the area of the diagram times the width gives the same force.
Centre of pressure
The point of application (the centre of pressure D) lies below the centroid C because the pressure is larger at the bottom. The shift along the wall is e = I_c / (l_C·A), where I_c is the second moment of area about the horizontal centroidal axis and l_C = h_C / sin α is the distance from the line where the wall plane meets the free surface to the centroid. For a rectangle I_c = b·a³/12, for a circle π·d⁴/64, for a triangle b·a³/36. A gauge pressure p₀ on the surface is replaced by a layer of liquid of height p₀/(ρg): the force grows and the centre of pressure moves towards the centroid.
Curved wall
For a cylindrical surface the force is split into components. The horizontal one is F_x = ρ·g·h_cx·A_x, where A_x is the projection of the wall on a vertical plane and h_cx is the depth of its centroid. The vertical one is F_z = ρ·g·V, where V is the volume of the pressure body bounded by the wall, the free surface and the verticals through the ends of the wall. If the pressure body is filled with liquid the force acts downward, if it is imaginary the force acts upward. For a circular arc all elementary forces are radial, so the resultant passes through the centre of the arc and its angle to the horizontal follows from tan φ = F_z / F_x.
Sources: Chugaev R. R. Hydraulics; Shterenlikht D. V. Hydraulics; White F. M. Fluid Mechanics; Streeter V. L. Fluid Mechanics.