A quadratic analytical solution of root pressure generation provides insights about bamboo and other species

We derived a steady-state model of whole root pressure generation through the combined action of all parallel segments of fine roots. This may be the first complete analytical solution for root pressure, which can be applied to complex roots/shoots. The osmotic volume of a single root is equal to that of the vessel lumen in fine roots and adjacent apoplastic spaces. Water uptake occurs via passive osmosis and active solute uptake ([Formula], osmol s-1), resulting in the osmolal concentration Cr (mol{middle dot}kg-1 of water) at a fixed osmotic volume. Solute loss occurs via two passive processes: radial diffusion of solute Km (Cr-Csoil), where Km is the diffusional constant and Csoil is the soil-solute concentration) from fine roots to soil and mass flow of solute and water into the whole plant from the end of the fine roots. The proposed model predicts the quadratic function of root pressure [Formula], where b and c are the functions of plant hydraulic resistance, soil water potential, solute flux, and gravitational potential. The present study investigates the theoretical dependencies of Pr on the factors detailed above and demonstrates the root pressure-mediated distribution of water through the hydraulic architecture of a 6.8-m-tall bamboo shoot. One sentence SummaryAn analytical solution for root pressure is derived and illustrated by applying it to the measured hydraulic architecture of a 7-meter bamboo shoot.