Hydrostatic stress Information & Hydrostatic stress Links at HealthHaven.com

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". Its magnitude $σ h$ can be given by:

$\sigma_h = \displaystyle\sum_{i=1}^n \rho_i g h_i$

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

$\sigma_{h,sand} = \rho_w g h_w = 1000 \text{kg/m}^3 \cdot 9.8 \text{m/s}^2 \cdot 10 \text{m} = 9.8 \cdot 10^4 {kg/ms^2} = 9.8 \cdot 10^4 {N/m^2}$

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

$\sigma_h \cdot I_3 = \left[ \begin{array}{ccc} \sigma_h & 0 & 0 \\ 0 & \sigma_h & 0 \\ 0 & 0 & \sigma_h \end{array} \right]$

where $I 3$ is the 3-by-3 identity matrix.