Root water uptake is driven by a combination of hydrostatic and osmotic forces. Water transport was characterized in primary roots of maize seedlings grown hydroponically under standard and water deficit (WD) conditions, as induced by addition of 150 g.L -1 polyethylene glycol-8000 (water potential= -0.336MPa). Flow measurements were performed by the pressure chamber technique in intact roots or on progressively cut root system architectures (RSA). To account for the concomitant transport of water and solutes in roots under WD, we developed within realistic RSAs a Hydraulic Tree Model integrating both solute pumping and leak. This model explains the high spontaneous sap exudation of roots grown in standard conditions, the non-linearity of pressure-to flow relationships, and negative fluxes observed under WD conditions at low external hydrostatic pressure. The model also reveals the heterogeneity of driving forces and elementary radial flows throughout RSA, and how this heterogeneity depends on both plant treatment and water transport mode. The full set of flow measurement data obtained in individual roots grown under standard or WD conditions was used in an inverse modeling approach to determine their respective radial and axial hydraulic conductivities. This approach allows to resolve dramatic effects of WD on these two components.