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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.
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).
The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For a horizontal device, the continuity equation shows that for an incompressible fluid, the reduction in diameter will cause an increase in the fluid flow speed.
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]
In fluid dynamics, two types of stream function are defined: The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, [ 1 ] is defined for incompressible ( divergence-free ), two-dimensional flows .
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a nearly constant volume independent of pressure. It is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape.
a property in thermodynamics and fluid dynamics, see Compressibility or Incompressible flow; a property of a vector field, see Solenoidal vector field; a topological property, see Incompressible surface; a proof method in mathematics, see Incompressibility method; a property of strings in computer science, see Incompressible string
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 ...