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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.
Submerged specific gravity is a dimensionless measure of an object's buoyancy when immersed in a fluid.It can be expressed in terms of the equation = where stands for "submerged specific gravity", is the density of the object, and is the density of the fluid.
(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.
In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh [1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. [2] [3] [4] It characterises the fluid's flow regime: [5] a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow.
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.
In fluid dynamics, the Boussinesq approximation (pronounced, named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by g , the acceleration due to gravity .
From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.