Hydrostatic Force acting on Submerged Surface

The thrust force acting on a surface submerged in a liquid can be calculated as

F = p_a A

= ρ g h_a A                           (1)

where

F = thrust force (N)

p_a = ρ g h_a = average pressure on the surface (Pa)

A = area of submerged surface (m²)

h_a = average depth (m)

ρ = density (kg/m³)  (water 1000 kg/m³)

g = acceleration of gravity (9.81 m/s²)

Example - The thrust force acting on the side of a container

The trust force acting on the submerged vertical side of a container can be calculated as

F = p_a A

= ((p_t + p_b ) / 2) A

= (ρ g (h_t + h_b ) / 2) A                      (2)

where

p_t = pressure at the top of the submerged surface (Pa)

p_b = pressure at the bottom of the submerged surface (Pa)

h_t = depth at the top of the submerged surface (m)

h_b = depth at the bottom of the submerged surface (m)

The thrust on a surface with width 1 m and height from 0 m to 2 m - in a water-filled container can be calculated as

F = (ρ g (h_t + h_b) / 2) A

= (1000 kg/m³) (9.81 m/s²) ((0 m) + (2 m)) / 2) ( (1 m) (2 m))

= 19620 N

= 19.6 kN

Example - The thrust force acting on the bottom of a container

The trust force acting on the horizontal bottom of a submerged container can be calculated as

F = p_b A

= ρ g h_b A                           (2b)

The thrust on a bottom with width 1 m and length 2 m - on depth 1 m - in a water filled container can be calculated as

F = ρ g h_b A

= (1000 kg/m³) (9.81 m/s²) (1 m) ( (1 m) (2 m))

= 19620 N

= 19.6 kN