Many methods have been proposed to extract pressure gradient maps from magnetic resonance (MR) images. They were based on the resolution of the haemodynamic model of Navier-Stokes and needed the flow acceleration to be known. Most used velocity data acquisition and computed acceleration from temporal and spatial derivatives of the velocity field. However, MR sequences have been developed in order to acquire the acceleration field directly. Here we compared direct MR measurements of acceleration field components with those calculated from MR velocity acquisitions. Two experimental phantoms were used to separately evaluate the inertial and convective components of the acceleration. Mathematical simulation of the convective phantom further explained the origin of the noise generated by the spatial and temporal derivatives of the velocity data, and the misregistration artefacts due to MR sequences. We found that direct measurement of the acceleration field generates less noise and fewer artefacts than calculation from velocity derivatives.