The suitability of the analysis for an unsteady compressible gas flow through an exhaust junction plays an important role in developing a computer program for the matching of a diesel engine to an exhaust turbocharger. The maximum momentary temperature difference between the lateral flow and the main flow at the junction is about 300°C in an actual engine. It is important to adopt boundary conditions compatible with the flow phenomena in order to improve the accuracy of the estimation of the exhaust energy. In previous works, the incompressible joining flow loss coefficients were employed in the computer program for the convenience of the calculation. In this study, the joining flow model of different kinds of gases has been assumed, and the flow loss coefficients are compared with incompressible ones. It is shown that the present results give the precise boundary conditions for the computer program.