In continuum mechanics, a hydrostatic stress is an isotropic stress that is given by the weight of water above a certain point. It is often used interchangeably with "pressure" and is also known as confining stress, particularly in the field of geomechanics. Its magnitude σ h can be given by:
σ h = ∑ i = 1 n ρ i g h i where i is an index denoting each distinct layer of material above the point of interest, ρ 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 h i 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
σ h = ρ w g h w = 1000 kg/m 3 ⋅ 9.8 m/s 2 ⋅ 10 m = 9.8 ⋅ 10 4 k g / m s 2 = 9.8 ⋅ 10 4 N / m 2 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
σ h ⋅ I 3 = [ σ h 0 0 0 σ h 0 0 0 σ h ] where I 3 is the 3-by-3 identity matrix.
