  More than five hundred years ago Leonardo Da Vinci found a pattern in the
growth of trees nowadays known as the Leonardo's rule. This rule relates the
thickness of the stem with the thickness of the branches at different
bifurcation stages in a Pythagorean fashion. He argued that his rule was the
result of the conservation of sap flux. In the present work, we explore this
idea by assuming that the sap flux through each xylem element behaves as a
non-ideal fluid and the size-distribution of the xylem elements obeys a power
law distribution. We find that the simultaneous fulfillment of Leonardo's rule
and the conservation of the sap flux, lead to a global behavior of the sap like
that of an ideal fluid after summing over all xylem elements. These results are
supported by field and experimental work. In particular, we corroborated the
Leonardo's rule in different tree species by measuring the stem-branches
thickness at different bifurcations stages. We also determined the statistical
size-distribution of the xylem elements through a maceration process, finding
that it corresponds to a power law distribution with an exponent close to
three, which is the exponent required for the Leonardo's rule. As far as we
know this is the first time that a statistical hydraulic model supported by
experimental data is presented for the Leonardo's rule.
