as $c_\mathrm{s}^{2}=\frac{p_\mathrm{gas}}{\rho}$ where $p_\mathrm{gas}$ is the gas pressure. Following AM12 and Zhang & Dai (2008), we introduce three component of Alfven sound speed $c_\mathrm{r},c_\mathrm{\varphi}$ and $c_\mathrm{z}$ as:

$$c_\mathrm{r,\varphi,z}^{2}=\frac{B_{r,\varphi,z}^{2}}{\textbf{4}\pi\rho}=\frac{2p_\mathrm{mag_{r,\varphi,z}}}{\rho}$$

where $B_{r,\varphi,z}$ and $p_\mathrm{mag_{r,\varphi,z}}$ are three components of magnetic field and magnetic pressure respectively.

By integration over $z$ of the azimuthal equation of motion gives.

$$\Sigma V_r \frac{d}{dr}(rV_\varphi)=-\frac{1}{r}\frac{d}{dr}(J_{vis})-\frac{1}{r}\frac{d}{dr}(J_{con})-  \frac{\Omega(lr)^{2}}{2\pi}\frac{d\dot{M_{w}}}{dr}$$

$$+r \sqrt{\Sigma} c_\mathrm{r}\frac{d}{dr}(\sqrt{\Sigma} c_\mathrm{\varphi})+\Sigma c_\mathrm{r} c_\mathrm{\varphi}$$

where $\Omega(=\frac{V_\varphi}{r})$ and are the angular and Keplerian velocities respectively. The third term on the right hand side shows the angular momentum carried a way by wind/outflow materials. Knigge (1999) define the $l$ parameter as the length of the rotational lever-arm that allows we have several types of accretion disc winds models. The parameter $l=0$ corresponds to a non-rotating wind and the angular momentum is not extracted by the wind and the disc losses only mass because of the wind while $l=1$ represents outflowing materials that carries away the specific angular momentum $(r^{2}\Omega)$. This latter would be most fitting value for radiation-driven wind (Proga et al. 1998). Centrifugally driven MHD wind/outflow are correspond to $l>1$ and it would be able to remove a lot of angular momentum of the discs.

The $J_{vis}$ and $J_{con}$ are the viscous 