A method and associated apparatus are disclosed for determining the location of an effective center of fluid flow in a vessel using an ultrasound apparatus. Ultrasound energy is propagated along an axis of propagation and projects upon the vessel. A Doppler-shifted signal reflected from the fluid in the vessel is received and a set of quantities expressed as a density is derived from the Doppler shifted signal for each of a set of coordinates, the density being a function of the Doppler shift in frequency associated with each of the coordinates. One of a mean, mode or median is calculated for each of the dimensions of the set of coordinates in conjunction with the density associated therewith. This calculation is repeated throughout the field of view of the vessel to define a centerline.