Xylem vessels (and tracheids) are not just pipes to carry water, they are pipes with holes in them (pits) through which water can leak out, fulﬁlling a principal leaf function of water distribution through the transpiration stream to places where it will evaporate. The branching network of vessels is beautifully adapted to achieve this.
Think about flow in a leaky vessel. As explained earlier, the rate of volume flow varies as the fourth power of the radius (Poiseuille’s Law). The frequency of leaks through vessel walls varies with surface area of the walls, that is, as the ﬁrst power of the radius (2πr). So if the vessel is wide, forward flow is much larger than leakage. The wide vessels in large veins supply water all over the leaf without losing much on the way. As the width of a vessel becomes smaller, the forward flow (a function of r4) is reduced much more strongly than the leaks (a function of r). The proportion of water lost to leakage therefore increases as vessels become smaller. Indeed, for a ﬁxed pressure gradient there is a critical radius at which all water entering the vessels supplies leaks, and there is no forward flow at all. The ﬁnest veins of dicotyledenous leaves have vessels of a radius that is close to this critical value. As sap disperses into the ﬁne ramiﬁcations of the network, it moves more and more slowly forward, and leaks increasingly outwards through the sheath to the mesophyll. This is the rationale of the distributing networks of the small branched veins of both dicotyledons and grasses.
Extraction of water from ﬁne veins can be readily demonstrated. Stand a cut leaf in an aqueous solution of dye, such as 0.1% sulphorhodamine G, and allow it to transpire for an hour. The solution moves rapidly through large veins all over the leaf in a few minutes. Then it moves increasingly slowly into the network of distributing small veins. By the end of an hour it has reached the ends of the ﬁnest veins and, as water is extracted from them, the dye becomes more and more concentrated (Figure 3.29). Movement of dyes from the ﬁnest veins to leaf surfaces 100 µm away takes about 30 min, suggesting that diffusion rather than mass flow is responsible for solute distribution to cells.