# 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 (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 *

## Related Topics

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Archimedes' Law

Forces acting on bodies submerged in fluids.

### Buoyancy

Buoyancy is the resultant force acting on a submerged body.

### Center of Gravity

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### Center of Gravity and Buoyancy

Stability - the center of gravity vs. the center of buoyancy.

### Hydrostatic Pressure vs. Depth

Depth and hydrostatic pressure.

### Underground Pipes - Earth Pressure

Pressure acting on underground pipes due to weight of soil and transport.