A mean field theory is developed for the Zimm model and compared to the exact solution, computed numerically, for the case of a single extended polymer. An analytic calculation in the dumbbell approximation extends the preaveraging treatment. We find that the dynamic scaling of the preaveraged Zimm model is preserved for short polymers, but that the relaxation function is inhomogeneous in length for long polymers. These calculations can be applied to recent experimental results.