For computing the component of the force in the x-direction, the dot product of the force and the unit vector ( i ) gives
                               
Where is the area projection of the curved element on a plane perpendicular to the x-axis. This integral means that each component of the force on a curved surface is equal to the force on the plane area formed by projection of the curved surface into a plane normal to the component.
The magnitude of the force component in the vertical direction (z direction)
                                     
Since and neglecting , we can write

                                    
in which is the weight of liquid above the element surface. This integral shows that the z-component of the force (vertical component) equals to the weight of liquid between the submerged surface and the free surface. The line of action of the component passes through the centre of gravity of the volume of liquid between the free surface and the submerged surface.