Euler equations

:This page discusses classical compressible fluid flow. For other uses, see Euler function (disambiguation)

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In fluid dynamics, the Euler equations govern the motion of a compressible, inviscid fluid. They correspond to the Navier-Stokes equations with zero viscosity, although they are usually written in the form shown here because this emphasises the fact that they directly represent conservation of mass, momentum, and energy. The equations are named for Leonhard Euler. This page assumes that classical mechanics applies; see relativistic Euler equations for a discussion of compressible fluid flow when velocities approach the speed of light.

Related Topics:
Fluid dynamics - Fluid - Navier-Stokes equations - Viscosity - Leonhard Euler - Relativistic Euler equations

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Although the Euler equations formally reduce to potential flow in the limit of vanishing Mach number, this is not helpful in practice, essentially because the approximation of incompressibility is almost invariably very close.

Related Topics:
Potential flow - Mach number

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In differential form, the equations are:

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:

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ablacdot( hoold u)=0

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:

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ablacdot( ho old u)old u+ abla p=0

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:

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ablacdot(old u(E+p))=0

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where E= ho e+ ho(u^2+v^2+w^2)/2 is the total energy per

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unit volume (e is the internal energy per unit mass for the

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fluid), p is the pressure, u the fluid velocity and

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ho the fluid density. The second equation includes the divergence of a dyadic tensor, and may be clearer in subscript notation:

Related Topics:
Divergence - Tensor

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:

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