We develop a parameter-free velocity-dependent one-scale model for the evolution of the characteristic length $L$ and root-mean-square velocity $sigma_v$ of standard domain wall networks in homogeneous and isotropic cosmologies. We compare the frictionless scaling solutions predicted by our model, in the context of cosmological models having a power law evolution of the scale factor $a$ as a function of the cosmic time $t$ ($a propto t^lambda$, $0< lambda < 1$), with the corresponding results obtained using field theory numerical simulations. We show that they agree well (within a few $%$) for root-mean-square velocities $sigma_v$ smaller than $0.2 , c$ ($lambda ge 0.9$), where $c$ is the speed of light in vacuum, but significant discrepancies occur for larger values of $sigma_v$ (smaller values of $lambda$). We identify problems with the determination of $L$ and $sigma_v$ from numerical field theory simulations which might potentially be responsible for these discrepancies.
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