Leaves lose approximately 400 H₂O molecules for every 1 CO₂ gained during photosynthesis. Most long-distance water transport in plants, or xylem sap flow, serves to replace this water to prevent desiccation. Theory predicts that the largest vessels contribute disproportionately to overall sap flow because flow in pipe-like systems scales with the fourth power of radius. Here, we confront these theoretical flow predictions for a vessel network reconstructed from X-ray μCT imagery with in vivo flow MRI observations from the same sample of a first-year grapevine stem. Theoretical flow rate predictions based on vessel diameters are not supported. The heterogeneity of the vessel network gives rise to transverse pressure gradients that redirect flow from wide to narrow vessels, reducing the contribution of wide vessels to sap flow by 15% of the total. Our results call for an update of the current working model of the xylem to account for its heterogeneity.