Consider a surface AB of an object submerged in a liquid (not necessarily water; the name hydrostatic force is, therefore, misnomer!). Top of the liquid-surface is exposed to atmosphere. The co-ordinate axis has been placed at the bottom of the liquid.
(Fig. 6a)
Pressure ‘p’ acts normal to the elemental surface, dA at a distance ‘z’
(differential force) acting on the surface
,
,
.This is the force acting only due to hydrostatic (liquid) pressure. Therefore,
.Such direct integration can be performed only for special (well-defined) geometries such as an arc of a circle because the normal to all arcs of the circle will pass through the center of the circle, or a horizontal surface because in such case .
It is easier to work on the vertical and horizontal components of the force separately.
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