Search results
Results from the WOW.Com Content Network
In fluid dynamics, a flow is considered incompressible if the divergence of the flow velocity is zero. However, related formulations can sometimes be used, depending on the flow system being modelled. Some versions are described below: Incompressible flow: =. This can assume either constant density (strict incompressible) or varying density flow.
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density.While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case). [1]
From a strictly aerodynamic point of view, the term should refer only to those side-effects arising as a result of the changes in airflow from an incompressible fluid (similar in effect to water) to a compressible fluid (acting as a gas) as the speed of sound is approached. There are two effects in particular, wave drag and critical mach.
For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3.
The mathematical characters of the incompressible and compressible Euler equations are rather different. For constant fluid density, the incompressible equations can be written as a quasilinear advection equation for the fluid velocity together with an elliptic Poisson's equation for the pressure.
Fluids may be classified by their compressibility: Compressible fluid: A fluid that causes volume reduction or density change when pressure is applied to the fluid or when the fluid becomes supersonic. Incompressible fluid: A fluid that does not vary in volume with changes in pressure or flow velocity (i.e., ρ=constant) such as water or oil.
For an incompressible and isotropic Newtonian fluid in laminar flow only in the direction x (i.e. where viscosity is isotropic in the fluid), the shear stress is related to the strain rate by the simple constitutive equation = where is the shear stress ("skin drag") in the fluid,
As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may change, [2] [3] and its shape changes due to distortion by the flow. [1] In an incompressible flow, the volume of the fluid parcel is also a constant (isochoric flow).