ESTIMATING VOLUME FLOW-RATES THROUGH XYLEM CONDUITS

We discuss the errors in common approximations of the volume how rate for laminar how through conduits with noncircular transverse sections. Before calculating how rates, ideal geometric shapes are chosen to represent the noncircular transverse sections. The Hagen-Poiseuille equation used with hydraulic diameter underestimates the volume flow rate for laminar how through conduits even with such ideal shapes. Correction factors that have been proposed for the Hagen-Poiseuille equation also lead to underestimates of the volume flow rate for those shapes. The exact solutions are sometimes difficult to attain, but rates calculated using the exact solutions for the ideal shapes may be as much as five times higher than the approximated rates for common transversely elongated shapes. Either the exact solutions or the approximations may be used to calculate volume flow rates through the xylem of plants. Both of these methods actually approximate how through the original conduits because the shapes used are approximations of the conduits' transverse sections. We recommend using the exact solutions whenever possible; they should be closer to the real solution than other approximations. We give tables of correction factors for use in the cases where calculating volume how rate from the approximate solution, the Hagen-Poiseuille equation, is more feasible. Obtaining theoretical volume flow rates that are larger than previously thought highlights the need to clarify the causes of differences between the theoretical rates and the smaller measured volume flow rates in plant xylem.