If an ultrasound beam uniformly insonates the cross section of a blood vessel then the Doppler signal can be analyzed to give a frequency proportional to the spatial mean blood velocity. This is also possible if the beam can be thought of as negligibly thin compared to the blood vessel radius, centrally placed, and the blood velocity profile is axisymmetric and monotonic, although the analysis takes a different form. The immunity of these mean velocity estimators to broadening of the ideal frequency spectrum is studied. If the broadening of a frequency component is such that its mean frequency, weighted by intensity, is unchanged then the analysis with a uniformly insonating beam still leads to the correct mean velocity. In contrast, for any such broadening, the analysis if the beam is negligibly thin produces an underestimate of the mean velocity. Error expressions are derived for idealized cases and some practical results given.