# Hydrostatic Forces acting on a Submerged Surface

## A thrust force will act on a 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 (m ^{2})*

*h _{a} = average depth (m)*

*ρ = density (kg/m ^{3}) (water 1000 kg/m^{3})*

*g = acceleration of gravity (9.81 m/s ^{2}) *

### 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/m ^{3}) (9.81 m/s^{2}) ((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/m ^{3}) (9.81 m/s^{2}) *

*(1 m) (*

*(1 m) (2 m))*

* = 19620 N*

* = 19.6 kN*