  Hot massive stars present strong stellar winds that are driven by absorption,
scattering and re\-emission of photons by the ions of the atmosphere
(\textit{line-driven winds}). A better comprehension of this phenomenon, and a
more accurate calculation of hydrodynamics and radiative acceleration is
required to reduce the number of free parameters in spectral fitting, to
determine accurate wind parameters such as mass-loss rates and velocity
profiles.
  We use the non-LTE model-atmosphere code CMFGEN to numerically solve the
radiative transfer equation in the stellar atmosphere and to calculate the
radiative acceleration $g_\text{rad}(r)$. Under the assumption that the
radiative acceleration depends only on the radial coordinate, we solve
analytically the equation of motion by means of the Lambert $W$-function. An
iterative procedure between the solution of the radiative transfer and the
equation of motion is executed in order to obtain a final self-consistent
velocity field that is no longer based on any $\beta$-law.
  We apply the Lambert-procedure to three O supergiant stars ($\zeta$-Puppis,
HD~165763 and $\alpha$-Cam) and discuss the Lambert-solutions for the velocity
profiles. It is found that, even without recalculation of the mass-loss rate,
the Lambert-procedure allows the calculation of consistent velocity profiles
that reduce the number of free parameters when a spectral fitting using CMFGEN
is performed. Synthetic spectra calculated from our Lambert-solutions show
significant differences compared to the initial $\beta$-law CMFGEN models. The
results indicate the importance of consistent velocity profile calculation in
the CMFGEN code and its usage in a fitting procedure and interpretation of
observed spectra.
