The Physics
Hypertextbook
Opus in profectus

# Buoyancy

## Summary

• Buoyancy (also known as the buoyant force) is the force exerted on an object that is wholly or partly immersed in a fluid.
• The symbol for the magnitude of buoyancy is B or FB
• As a vector it must be stated with both magnitude and direction.
• Buoyancy acts upward for the kind of situations encountered in everyday experience.
• As with other forces, the SI unit of buoyancy is the newton [N].
• Buoyancy is caused by differences in pressure acting on opposite sides of an object immersed in a static fluid.
• A typical situation:
1. The pressure on the bottom of an object is greater than the top (since pressure increases with depth).
2. The force on the bottom pushes up and the force on the top pushes down (since force is normal to the surface).
3. The direction of the net force due to the fluid is upward.
• Pressure variations in a fluid are typically caused by gravity (since P = P0 + ρgh), but in general buoyant forces act opposite the direction of the frame of reference acceleration.
• Under conditions of apparent weightlessness there can be no buoyant forces.
• Archimedes' Principle
• The magnitude of the buoyant force on an object is equal to the weight of the fluid it displaces.

B = ρgVdisplaced

• The factors that affect buoyancy are…
• the density of the fluid
• the volume of the fluid displaced
• the local acceleration due to gravity
• The buoyant force is not affected by…
• the mass of the immersed object
• the density of the immersed object
• Objects immersed in a fluid have an apparent weight that is…
• reduced by the buoyant force (less than their actual weight)

W′ = W − B (W′ < W)

• directly proportional to the relative density (ρ′ = ρobject − ρfluid)

W′ = ρ′gV

Buoyancy and density
densities B > Wobject B = Wobject B < Wobject
ρobject < ρfluid object rises
(wholly immersed )
float on surface
(partly immersed)
ρobject = ρfluid neutral buoyancy
(wholly immersed)
ρobject > ρfluid object sinks