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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.
At a stagnation point, the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy. In both compressible and incompressible fluid flow, the stagnation temperature equals the total temperature at all points on the streamline leading to the stagnation point.
The incompressible flow assumption typically holds well with all fluids at low Mach numbers (say up to about Mach 0.3), such as for modelling air winds at normal temperatures. [16] the incompressible Navier–Stokes equations are best visualized by dividing for the density: [17]
The flow is incompressible and Newtonian. Coordinates are orthogonal. Flow is 2D: u 3 = ∂u 1 / ∂x 3 = ∂u 2 / ∂x 3 = 0; The first two scale factors of the coordinate system are independent of the last coordinate: ∂h 1 / ∂x 3 = ∂h 2 / ∂x 3 = 0, otherwise extra terms appear. The stream function has ...
The Poiseuille flow theorem [7] is a consequence of the Helmholtz theorem states that The steady laminar flow of an incompressible viscous fluid down a straight pipe of arbitrary cross-section is characterized by the property that its energy dissipation is least among all laminar (or spatially periodic) flows down the pipe which have the same total flux.
Thus for an incompressible inviscid fluid the specific internal energy is constant along the flow lines, also in a time-dependent flow. The pressure in an incompressible flow acts like a Lagrange multiplier, being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no ...
Density variation due to both concentration and temperature is an important field of study in double diffusive convection. If density changes due to both temperature and salinity are taken into account, then some more terms add to the Z-Component of momentum as follows: [ 7 ] [ 8 ]
As the temperature from both sides of the shock wave is discontinuous, the speed of sound is different in these adjoining medium. So it is convenient to define the star mach number that will be independent of the specific mach number. From star condition, the speed of sound at the critical condition can also be a good reference velocity.