We used dedicated magnetic resonance imaging (MRI) equipment and methods to study phloem and xylem transport in large potted plants. Quantitative flow profiles were obtained on a per-pixel basis, giving parameter maps of velocity, flow-conducting area and volume flow (flux). The diurnal xylem and phloem flow dynamics in poplar, castor bean, tomato and tobacco were compared. In poplar, clear diurnal differences in phloem flow profile were found, but phloem flux remained constant. In tomato, only small diurnal differences in flow profile were observed. In castor bean and tobacco, phloem flow remained unchanged. In all plants, xylem flow profiles showed large diurnal variation. Decreases in xylem flux were accompanied by a decrease in velocity and flow-conducting area. The diurnal changes in flow-conducting area of phloem and xylem could not be explained by pressure-dependent elastic changes in conduit diameter. The phloem to xylem flux ratio reflects what fraction of xylem water is used for phloem transport (Münch’s counterflow). This ratio was large at night for poplar (0.19), castor bean (0.37) and tobacco (0.55), but low in tomato (0.04). The differences in phloem flow velocity between the four species, as well as within a diurnal cycle, were remarkably small (0.25–0.40 mm s−1). We hypothesize that upper and lower bounds for phloem flow velocity may exist: when phloem flow velocity is too high, parietal organelles may be stripped away from sieve tube walls; when sap flow is too slow or is highly variable, phloem-borne signalling could become unpredictable.