Thermal models of subduction zones, restrict the melt source region to a domain at sufficiently high temperature with water present (either as a free phase or in hydrous minerals). Water, released into the mantle by slab dehydration, traverses the wedge horizontally by a combination of (i) vertical movement as a fluid phase and (ii) fixed in amphiboles carried by the induced mantle flow; only in mantle hotter than amphibole stability can melts escape upwards. We develop a one-dimensional model for the source region fluxed with water. The induced mantle flow advects heat laterally to balance the latent heat of melting, in a column where the liquidus of the melt is depressed by its water content. Melt flux, fraction, temperature and water content are calculated assuming steady state. Melt compositions are predicted from the melt fraction distribution as a function of depth, constrained by the experimental data of Green. On investigating a range of plausible models, we find that the average degrees of melting predicted vary from ca. 2 to 8%. The predicted primary magmas are mafic high magnesium basalts with water contents ranging from 1.6 to 6 wt%, and temperatures from 1160 to 1290 degrees C. Models with shallower depths of segregation have higher degrees of melting and lower water contents. The volumes predicted by the physical model are a strong function of the water flux assumed to enter the source region. Previous estimates of arc growth would suggest either low water fluxes or that not all the melt reaches the arc crust.