We present a new derivation of the CORS Baade–Wesselink method in the Walraven photometric system .
We solved the complete Baade–Wesselink equation by calibrating the surface brightness function with a recent grid of atmosphere models .
The new approach was adopted to estimate the mean radii of a sample of Galactic Cepheids for which are available precise light curves in the Walraven bands .
Current radii agree , within the errors , quite well with Cepheid radii based on recent optical and near–infrared interferometric measurements .

We also tested the impact of the projection factor on the Period–Radius relation using two different values ( p = 1.36 , p = 1.27 ) that bracket the estimates available in the literature .
We found that the agreement of our Period–Radius relation with similar empirical and theoretical Period–Radius relations in the recent literature , improves by changing the projection factor from p = 1.36 to p = 1.27 .
Our Period–Radius relation is \log R = ( 0.75 \pm 0.03 ) \log P + ( 1.10 \pm 0.03 ) , with a rms = 0.03 dex .

Thanks to accurate estimates of the effective temperature of the selected Cepheids , we also derived the Period–Luminosity relation in the V band and we found M _ { V } = ( -2.78 \pm 0.11 ) \log P + ( -1.42 \pm 0.11 ) with rms = 0.13 mag , for p = 1.27 .
It agrees quite well with recent results in the literature , while the relation for p = 1.36 deviates by more than 2 \sigma .
We conclude that , even taking into account the intrinsic dispersion of the obtained Period–Luminosity relations , that is roughly of the same order of magnitude as the effect of the projection factor , the results of this paper seem to favour the value p = 1.27 .