Abstract: The development of non-invasive medical technology such as B-mode ultrasound has allowed direct real time imaging of blood vessels. This enables individual patient arterial responses to be recorded and analyzed following pharmacologic perturbations. By analysis of intra- arterial pressure recordings together with recording of the pulse wave speed, the spatial pressure gradient can be approximated. The spatial pressure gradient together with the internal vessel radius from B-mode imaging permits calculation of the vessel volume flow by Womersley analysis. The Womersley solution is the only analytical solution of a time varying flow, which is assumed to be laminar, fully developed and Newtonian in an infinitely long rigid tube. We approximated the internal arterial radius by averaging the peak systolic arterial radius and the end diastolic radius following their estimation using a spatial cross- correlation function of the arterial B-mode images. Womersley extended the analysis to elastic tubes and we present illustrative calculations of both the rigid and elastic tube models however,only the rigid tube model has been experimentally validated.