$$V\frac{\partial V}{\partial r} +\frac{U}{r}\frac{\partial V}{\partial \theta} -\frac{U^{2}}{r}=
-\frac{1}{\rho}\frac{\partial P}{\partial r} - \frac{G M}{r^{2}},$$

$$V\frac{\partial U}{\partial r} +\frac{U}{r}\frac{\partial U}{\partial \theta} +\frac{V U}{r}=
-\frac{1}{r \rho}\frac{\partial P}{\partial \theta},$$

for the continuity equation, and the radial and angular components of Euler’s equation. In the above, $V$, $U$, $\rho$ and $P$ give the radial velocity, angular velocity, matter density and pressure, respectively. We have neglected temporal derivatives, as we are interested at this point, in the characteristics of steady state solutions. We take as a background state a free-falling axially symmetrical distribution of cold gas, described by $V_{0}=-(2GM/r)^{1/2}$, $U_{0}=0$ and $\nabla \vec{P_{0}}=0$, a consistent solution to eqs.(15) and (16). Having ignored the inclusion of the radius at which the transition to radial flow takes place in the choice of $V_{0}$ limits the validity of the analysis to radial scales along the plane of the disk much smaller than $R_{T}$. This is justified by the fact that jets appear as phenomena extremely localised towards $R \rightarrow 0$. We now take a density profile given by:

$$\rho_{0}(r,\theta)=f(r)g(\theta),$$

were $f(r)$ is a dimensionless function of $r$ and $g(\theta)$ describes the polar angle dependence of the infalling material, for example, one can ask for $g(\theta=\pi/2)=\bar{\rho}_{0}$, diminishing symmetrically towards the 