Incompressible fluid

In fluid mechanics, an incompressible fluid is a fluid whose density (often represented by the Greek letter ρ) is constant: it is the same throughout the field and it does not change through time. It is an idealization used to simplify analysis. In reality, all fluids are compressible to some extent.

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Partial differential equations for incompressible fluids are as follows:

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: {partial ho over partial t} = 0,

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: {partial ho over partial x} = 0,

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: {partial ho over partial y} = 0,

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: {partial ho over partial z} = 0.

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The last three equations imply that the gradient of the density of an incompressible fluid is zero:

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: abla ho = 0 .

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The continuity equation can be applied to obtain another criterion for an incompressible fluid: the divergence of the velocity field v of an incompressible fluid is zero.

Related Topics:
Continuity equation - Divergence

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