Fluid Equations in Cartesian Coordinates

(1.127) | ||

(1.128) | ||

(1.129) | ||

(1.130) | ||

(1.131) | ||

(1.132) |

where is the velocity, the pressure, and the viscosity. The equations of compressible fluid flow, (1.87)-(1.89) (from which the equations of incompressible fluid flow can easily be obtained by setting ), become

(1.133) | ||

(1.134) | ||

(1.135) | ||

(1.136) | ||

(1.137) |

where is the mass density, the ratio of specific heats, the heat conductivity, the molar mass, and the molar ideal gas constant. Furthermore,

(1.138) | ||

(1.139) | ||

(1.140) | ||

(1.141) |

Here, , , , and are treated as uniform constants.