Plants have highly effective vascular systems, which can transport fluid over large
distances. The xylem system carries water from the roots up to the leaves and the phloem
system carries sugar solutions from sugar sources (leaves) to sugar sinks (roots, fruits etc.)
and thus provides the necessary material for growth. There are many important fluid
dynamical problems connected with these flows, and I shall discuss some of them. In the
1920ies, Ernst Münch proposed that sugar transport in the phloem is driven by passive
osmotic pressure gradients generated by loading and unloading sugar into the phloem
tubes (sieve elements) of the leaves. It has been strongly debated whether this hypothesis
can actually account for long distance translocation, e.g., all the way from canopy to root
of a large tree. In the lecture, I will argue that optimization of the efficiency of the sugar
transport leads to a universal scaling of the width of the phloem tubes with the loading
(leaf) length and the translocation (stem) length in plants. These predictions have been
tested for plants ranging from 10 cm herbacious plants to 60 m trees - both hardwood and
conifers - and provide the first quantitative test of Münchs ideas. For both the xylem and
the phloem, the leaves provide the driving force for the sap flow, and I shall discuss
current ideas how this complex feat is accomplished.