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# Fluid Equations in Cartesian Coordinates

Let us adopt the conventional Cartesian coordinate system, ( , , ). According to Equation (1.26), the various components of the stress tensor are  (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.   Next: Fluid Equations in Cylindrical Up: Mathematical Models of Fluid Previous: Dimensionless Numbers in Compressible
Richard Fitzpatrick 2016-03-31