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The momentum equation in the direction of gravity should be modeled for buoyant forces resulting from buoyancy. [1] Hence the momentum equation is given by ∂ρv/∂t + V.∇(ρv)= -g((ρ-ρ°) - ∇P+μ∇ 2 v + S v. In the above equation -g((ρ-ρ°) is the buoyancy term, where ρ° is the reference density.
(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.) Example: If you drop wood into water, buoyancy will keep it afloat. Example: A helium balloon in a moving car. When increasing speed or driving in a curve, the air moves in the opposite direction to the car's acceleration.
Buoyancy (/ ˈ b ɔɪ ən s i, ˈ b uː j ən s i /), [1] [2] or upthrust is a net 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.
Buoyancy effects, due to the upward force on the object by the surrounding fluid, can be taken into account using Archimedes' principle: the mass has to be reduced by the displaced fluid mass , with the volume of the object.
An object immersed in a liquid displaces an amount of fluid equal to the object's volume. Thus, buoyancy is expressed through Archimedes' principle, which states that the weight of the object is reduced by its volume multiplied by the density of the fluid. If the weight of the object is less than this displaced quantity, the object floats; if ...
If it is much greater than unity, buoyancy is dominant (in the sense that there is insufficient kinetic energy to homogenize the fluids). If the Richardson number is of order unity, then the flow is likely to be buoyancy-driven: the energy of the flow derives from the potential energy in the system originally.
The buoyancy depends upon the difference of the densities (ρ air) − (ρ gas) rather than upon their ratios. The lifting force for a volume of gas is given by the equation: F B = (ρ air - ρ gas) × g × V. Where F B = Buoyant force (in newton); g = gravitational acceleration = 9.8066 m/s 2 = 9.8066 N/kg; V = volume (in m 3).
Pure jets and pure plumes define flows that are driven entirely by momentum and buoyancy effects, respectively. Flows between these two limits are usually described as forced plumes or buoyant jets. "Buoyancy is defined as being positive" when, in the absence of other forces or initial motion, the entering fluid would tend to rise.