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P_1 = \frac{3}{4} \rho_0 v_0^2  \end{equation}  In our case we are dealing with an oblique shock (Figure~\ref{fig:sketch}. (Figure~\ref{fig:sketch}).  Equations~\ref{RH1} to \ref{eqn:4} stay valid if only the velocity component perpendicular to the shock front is taken as $v_0$ and $v_0$. Figure~\ref{fig:sketch} shows the geometry of the problem. We use a cylindrical coordinate system with an origin on the central star. We place the $z$-axis along the jet outflow direction and assume rotational symmetry around the jet axis. Thus, the flow can effectively be written in $(z,\omega)$.   We treat the disk wind as an outer boundary condition with a given pressure profile and concentrate on the description of the stellar wind. To simplify the equations we adopt Kompaneets' approximation \citep{1960SPhD....5...46K} which states that there is no axial pressure gradient so that the pressure profile of the disk wind, which is given as a boundary condition, extends through all layers of the outflow: