In continuum mechanics, a hydrostatic stress is an isotropic stress that is given by the weight of the material above a certain point. It is often used interchangeably with “pressure” and is also known as confining stress, particularly in the field geomechanics. Its magnitude ?h can be given by:
where i is an index denoting each distinct layer of material above the point of interest, ?i is the density of each layer, g is the gravitational acceleration (assumed constant here; this can be substituted with any acceleration that is important in defining weight), and hi is the height (or thickness) of each given layer of material. For example, the magnitude of the hydrostatic stress felt at a point under ten meters of fresh water would be
where the index w indicates “water”.
Because the hydrostatic stress is isotropic, it acts equally in all directions. In tensor form, the hydrostatic stress is equal to
where I3 is the 3-by-3 identity matrix.