FromPoiseuille's law of laminar pipe flow and simple algebra a formula is obtained in eq. [16] which gives the total pressure drop occuring in a “regular, branched pipe system”. By definition regularity is here understood to mean, that all branchings and all pipes between them are geometrically similar (fig. 1). The pressure drop is found to be independent of the system's internal structure, e.
... [Show full abstract] g. of the manifold type of the branchings. It only depends on the entrance and exit cross sections and numbers, on the volume contained in the system and on the flow rate and viscosity.
The distribution of blood pressure in the human systemic circulation (time mean values reduced to heart level) is then considered. Both arteries and veins are approximately taken to be “regular, branched pipe systems”. The small vessels: arterioles, capillaries and venules are treated separately, a lower apparent viscosity there being accounted for. The main pressure drop is shown to occur in the small vessels. It must be augmented by contraction of the arterioles and small arteries (vasotonus) in order to obtain the physiological pressure in the aorta. According to the calculations the internal diameter of the arterioles of a resting human should be in the range of 11 to 12μ. A plot is given (according to either of two idealized assumptions concerning the mode of contraction) of the aorta pressure as a function of both the arterioles' diameter and the heart flow rate (fig. 5).