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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.
ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by
Pressure in water and air. Pascal's law applies for fluids. Pascal's principle is defined as: A change in pressure at any point in an enclosed incompressible fluid at rest is transmitted equally and undiminished to all points in all directions throughout the fluid, and the force due to the pressure acts at right angles to the enclosing walls.
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. On the other hand, the compressible Euler equations form a quasilinear hyperbolic system of conservation equations .
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 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
In fluid dynamics, the pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own unique pressure coefficient, C p.
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 ]