Velocity-diameter relationships of the microcirculation.

An analytical expression for the relationship between velocity (and blood flow) and diameter for vessels in the microcirculatory range up to 900 mum diameter is presented. Both the arterial and venous systems are considered. The analytical expression for these relationships has been derived from computer analysis of data obtained from individual measurements reported in the literature. Computer analysis shows that blood velocity is a nearly linear function of diameter of blood vessels for the arteriolar tree. The relationship for blood flow as a function of diameter is Q = 108d3.101 for arteries, arterioles and capillaries in the diameter range 5 to 900 mum and for the venous system in the range 5 to 115 mum is Q = 334d2.388 where Q is in mum3 per second and d is in mum. Comparison of the results of this study for the arterial system to the Hagen-Poiseuille Law reveals close agreement, if correction is made for geometric factors of blood vessels and for the variation of viscosity with diameter for blood.