Hydrostatic fluid

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In atmospheric dynamics and fluid dynamics, a hydrostatic fluid is a fluid in which fluid stresses act isotropically and fluid elements are in local equilibrium with one another. Thus, all directional fluid stresses, normally represented as vectors, can be summarized by a scalar quantity called the hydrostatic pressure, which can still depend on position.

The stress tensor takes on the form:

{\sigma_{ij}} = -p{\delta_{ij}}\ ,

where:

p is the hydrostatic pressure, and {\delta_{ij}}\ is the kronecker delta


The equilibrium which exists in a hydrostatic fluid is often the result of a balance between forces that compress the fluid and forces that resist compression. For example, on earth, the atmosphere is compressed against the surface by gravity and supported by its internal energy. This is often referred to as hydrostatic equilibrium.