Figure 4.
(a) In vivo determined phloem flow rates (black dots) in petioles (one stem) of six species plotted as a function of phloem radius as later determined on the same plant material. The velocities vary as much as 2.5 orders of magnitude, from 3 µm s−1 (0.01 m h−1) in T. virginiana to 150 µm s−1 (0.6 m h−1) in Solanum lycopersicum. The model predictions (grey dots) calculated from equations (3.5)–(3.7) agree well with the observed data. The error bars indicate the mean and standard errors of N = 3–8 measurements. (b) Log–log plot of l1l2 versus measured radius r (black dots) for 20 plants of sizes ranging from r = 1 µm (T. virginiana) to r = 40 µm (Cucurbita pepo) and l2 = 0.1 m (T. virginiana) to l2 = 40 m (Robinia pseudoacacia). The prediction of equation (3.8) (thick black line) with parameters Lp = 5 × 10−14 m (Pa s)−1 and η = 5 × 10−3 Pa s (kinematic viscosity = 1.85 × 10−3, sieve plate factor = 2.7) is plotted along with the best fit to the plant data (dashed line, slope 2.6 ± 0.3), showing that the scaling relationship predicted by equation (3.8) falls within the 95% confidence interval (dotted lines). The error bars indicate the standard error in the radius r and lengths l1 and l2. See table 2 for further details on the species used.