Hydrostatic Thrust

On a Plane Surface

Acts normal to the surface on the centre of pressure with a magnitude of:

is the centroid of the submerged area. is the pressure at the centroid.

Centre of Pressure

Here:

• - Total submerged area
• - Distance to centre of pressure measured along the submerged surface from the free surface
• - Distance to measured along the submerged surface from the free surface
• - Second moment of submerged area about the centroidal axis parallel to the free surface

For a plane surface

For common shapes

Shape	Description
Parallelogram	Base . Height . Base is at the free surface.
Triangle	Base . Height . Base is at the free surface.
Circle	Radius . Center is at a depth .

Proof

Note

is the free surface (waterline plane). It is not a surface inside the fluid. It’s drawn like that for ease of reference.

Direction

All forces acting on the surface is normal to the surface. Therefore is normal to the surface.

Magnitude

Line of action

On a Curved Surface

Proof

For the equilibrium of the fluid volume .

For the equilibrium of the fluid volume .

Tensile stress in pipe

For a pipe with inner diameter and thickness containing a liquid under pressure , experiences a tensile stress: