Steady-state, quasi-one-dimensional conservation equations

Steady-state, quasi-one-dimensional conservation equations 

The equations governing the steady state, quasi-one-dimensional flow of a reacting gas with negligible transport properties can easily be obtained from equations (l-19)-(l-22). When transport by diffusion is negligible 0 and Dtj 0 for ij = 1. N the diffusion velocities, of course, vanish [FJ 0 for / = 1. N, see equation (1-14)]. If, in addition, transport by heat conduction is negligible (A 0) and = 0, then the heat flux q vanishes [see equation (1-15)]. Finally, in inviscid flow 0 and K 0), equations (1-16)-(1-18) show that all diagonal elements of the pressure tensor reduce to the hydrostatic pressure, pu = pjj — P33 = P-The steady-state forms of equations (1-20), (l-21a), and (1-22) then become 

The form assumed by the continuity equation, equation (1-19), can be derived formally by integration over the total cross-sectional area of the flow. The limits of the coordinates X2 and X3 [which appear in equation (1-13)] in such an integration must be independent of x because the boundaries of the cross section are streamlines and must therefore be parallel to the local X coordinate (that is, parallel to the local velocity vector). Thus, since the flow variables are independent of the coordinates X2 and X3, multiplication of equation (1-19) by 2 3 followed by integration over the cross-sectional area shows that 

For a number of purposes it is convenient to replace equation (6) by an alternative expression. If equation (A-5) is applied to a closed system consisting of a unit mass of the reacting fluid, then we obtain 

Reactions in Flows with Negligible Molecular Transport 

The equations governing the steady-state, quasi-one-dimensional flow of a reacting gas with negligible transport properties can easily be obtained from equations (l-19)-(l-22). When transport by diffusion is negligible (D,j 0 and Dr,i 0 for i,j = 1. N), the diffusion velocities, of course, vanish - 0 for j = see equation (1-14)]. If, in addi- 

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