The Upward Force of Fluids
Buoyancy is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus, the pressure at the bottom of a column of fluid is strictly greater than at the top.
This fundamental difference in pressure results in a net upward force acting on the object. The absolute magnitude of this buoyant force is proportional to the pressure difference, and is exactly equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object.
The Science of Floating
Whether an object floats or sinks is determined entirely by the battle between two forces:
- Gravity (Weight): Pulls the object down. It depends on the object's total mass.
- Buoyancy: Pushes the object up. It depends on the volume of fluid the object displaces.
If the buoyant force is greater than the object's weight, it floats. If it's less, it sinks. If they are exactly equal, the object is neutrally buoyant and will hover perfectly in the middle of the fluid, which is exactly how submarines and SCUBA divers maintain depth.
The Formula
Example Calculation
A completely submerged steel ball displaces exactly $0.5 , ext{m}^3$ of freshwater (density $1000 , ext{kg/m}^3$).
- Multiply Density $cdot$ Volume $cdot$ Gravity: $1000 cdot 0.5 cdot 9.81 = 4905 , ext{Newtons}$.
The water exerts an upward buoyant force of $4905 , ext{N}$ on the steel ball, effectively making it feel $4905 , ext{N}$ lighter while it remains underwater.