# Buoyancy

## The resultant force acting on a submerged body

Buoyancy is defined as the tendency of a body to float or rise when submerged in a fluid. The resultant force acting on a submerged body by the fluid is called the * buoyant force *and can be expressed as

F = V γ

=V ρ g(1)

where

F = buoyant force (N)

V = body volume (m^{3})

γ =ρg = specific weight of fluid (N/m^{3})

ρ= density of fluid (kg/m^{3})

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

The buoyant force acts upwards.

Archimedes' principle indicates that

*"the upward buoyant force that is exerted on a body fully or partially submerged in a fluid - equals to the weight of the fluid that the body displaces"*

- if the body weighs more than the fluid - it sinks
- if the body weighs less than the fluid - it floats

### Example - Buoyant Force acting on a Floating Box

A plastic box with length *0.3 m* and width *0.4 m* is submerged *0.1 m* into water. The water density is *1000 kg/m*^{3}.

The buoyant force acting on the box can be calculated with *(1) *

*F = (0.3 m) (0.4 m) (0.1 m) ( 1000 kg/m^{3}) (9.81 m/s^{2})*

* = 119 N*