Treatment of the equations of gaseous behaviour at rest is generally taken, as in hydrostatics, to begin with a consideration of the general equations of momentum for fluid flow, which can be expressed as: \rho [{\partial U_j\over\partial t} + U_i {\partial U_j\over\partial t}] = -{\partial P\over\partial x_j} - {\partial \tau_{ij}\over\partial x_i} + \rho g_j , where \rho is the mass density of the fluid, U_j is the instantaneous velocity, P is fluid pressure, g are the external body forces acting on the fluid, and \tau_{ij} is the momentum transport coefficient. As the fluid's static nature mandates that U_j = 0 , and that \tau_{ij} = 0 , the following set of
partial differential equations representing the basic equations of aerostatics is found. {\partial P\over\partial x_j} = \rho g_j However, the presence of a non-constant density as is found in gaseous fluid systems (due to the compressibility of gases) requires the inclusion of the
ideal gas law: {P\over\rho} = RT , where R denotes the universal gas constant, and T the temperature of the gas, in order to render the valid aerostatic partial differential equations: {\partial P\over\partial x_j} = \rho \hat{g_j} = {P\over\ RT} \hat{g_j}, which can be employed to compute the pressure distribution in gases whose thermodynamic states are given by the equation of state for ideal gases. == Fields of study ==