Hydrostatic Pressure

Hydrostatic pressure is the pressure at depth from the weight of the overlying fluid, given by the hydrostatic balance dp/dz = -rho g. Integrated downward, p = p_atm + integral of rho g dz, so pressure rises about 1 decibar per meter in seawater (10^4 pascals per meter), and 4,000 meters depth corresponds to roughly 4,000 decibars. The hydrostatic approximation holds whenever vertical accelerations are small against gravity, which is true for large-scale ocean flow and underlies the primitive equations and the Boussinesq system. Non-hydrostatic models are needed only at convection and small-scale wave scales.