Curved Surfaces

To solve forces on a curved surface we need to define a control volume of the fluid in order to examine the vertical and horizontal forces on the curved surface, as shown below.

Equations-

Horizontal component of force (force on projected area): FH = Fx= ρghA

Vertical component of force (force on projected area + weight): Fv = Fy + W

Therefore, the resultant force is: FR = √((FH)2 + (FV)2)

And the angle is: tan(a) = Fv/FH

Curved surface above:

If the curved surface is above the liquid then the weight of the liquid will act in the opposite direction.

Therefore, weight must be subtracted from the vertical component of the force rather than added.

Circular Surface:

For a circular surface (a curved surface with a constant radius), pressure force acts perpendicular to the surface therefore all of the pressure force is pointing towards the centre of the circle so the force also acts in the same direction.