We model the growth of ZnO nanowires via vapour phase transport and examine the relationship predicted between the nanowire length and radius. The model predicts that the lengths of the nanowires increase with decreasing nanowire radii. This prediction is in very good agreement with experimental data from a variety of nanowire samples, including samples showing a broad range of nanowire radii and samples grown using a lithographic technique to constrain the nanowire radius. The close agreement of the model and the experimental data strongly support supporting the inclusion of a surface diffusion term in the model for the incorporation of species into a growing nanowire.