# buoyancy

Buoyancy (buoyancy) is a force that acts on an object in a fluid such as water in the opposite direction of gravity.
The cause of buoyancy is explained by Archimedes' principle. An object is under pressure (hydrostatic pressure) from a fluid. At this time, the pressure differs between the top and bottom of the object (like the pressure at the top and foot of Mt. Fuji), and the force received from below is greater. Buoyancy is the difference between the upper and lower forces that this object receives. That is, an upward force acts on the object.

## Formulation

The buoyancy that an object receives is equal to the force of gravity acting on the same volume (surrounding) fluid as the object. That is, it becomes as follows.
F
b b
ρ
f
V
g
{\ displaystyle F_ {b} \ rho _ {f} Vg}
Fb: Buoyancy (N, kg · m / s²)
ρf: Fluid density (kg / m³)
V: Volume of object (m³)
g: Gravity acceleration (m / s²) The divergence theorem is used for the exact derivation of this equation.
Furthermore, if the density of the object is ρs, the resultant force of gravity and buoyancy acting on the object (assuming positive upwards) is
F
((
ρ
f
−
ρ
s
)
V
g
{\ displaystyle F (\ rho _ {f}-\ rho _ {s}) Vg}
Will be. therefore
When an object is lighter than a fluid (ρs <ρf), F> 0, that is, the object floats.
It can be seen that when an object is heavier than a fluid (ρs> ρf), F <0, that is, the object sinks.

## Dimensionless number

Among the dimensionless quantities used in fluid mechanics, the ones related to buoyancy are as follows. Both represent the ratio of magnitude to some other force.
Richardson number-ratio to inertial force
Grashof number-ratio to viscous force
Rayleigh number-ratio to heat diffusion
Eötvös number-ratio to surface tension

## Related items

Archimedes' principle
Liquefaction
ship
Airships, balloons, balloons
Lift