A new approach is presented to evaluate the velocity of field-driven domain walls by means of ab initio parameters. This approach makes intensive use of multi-scaling by means of (a) mapping of domain wall formation energies obtained in terms of a fully relativistic method onto a Landau-Ginzburg-type expression, and (b) applying the Landau-Lifshitz-Gilbert equation to evaluate the time needed to move domain walls. In comparison with the ``classical{''} expression for the domain wall velocity originally proposed by Landau and Lifshitz, according to which the velocity increases with increasing width of the domain wall, three different types of magnetic alloys, namely permalloy (Ni85Fe15), CoxNi(1-x) and CoxPd(1-x), are analyzed. It is shown that the Landau-Lifshitz expression for the velocity seems to be valid whenever the slopes of the exchange and the anisotropy energy with respect to the concentration are either both increasing or both decreasing.