Considerations on static pressure gradients in closed circulatory systems

Siphons are devices that transport liquids uphill between two containers. It has been proposed that a siphon principle operates in closed circulatory systems, as best exemplified by the circulation of blood in mammals. This principle is supposed to ensure that no additional work is necessary to pump blood above the level of the heart, and that there is no gravitational static pressure gradient in the column of blood. The first statement is correct, while we demonstrate that, ignoring hydraulic resistance to blood flow, the static pressure gradient is equal to the hydrostatic gradient in a siphon model of blood circulation, although the details of the proof do not depend on the geometry of the circulatory system and the proof can be trivially extended to other models such as a vascular waterfall. This implies that the controversy over the siphon principle has no implications for the description of blood circulation, and that mechanisms such as the "baffle," which some authors have appealed to in order to obtain the expected gradient, are not necessary. In our discussion, we also discuss empirical data that appear to provide additional verification of our results, as well as several everyday occurrences that provide additional support.