On connecting large vessels to small. The meaning of Murray's law.
A large part of the branching vasculature of the mammalian circulatory and respiratory systems obeys Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. Where this law is obeyed, a functional relationship exists between vessel radius and volumetric flow, average linear velocity of flow, velocity profile, vessel-wall shear stress, Reynolds number, and pressure gradient in individual vessels. In homogeneous, full-flow sets of vessels, a relation is also established between vessel radius and the conductance, resistance, and cross-sectional area of a full-flow set.
D000818:Animals; D001158:Arteries / Q000502:physiology; D001809:Blood Viscosity; D002320:Cardiovascular Physiological Phenomena; D004285:Dogs; D008433:Mathematics; D008954:Models, Biological; D012143:Respiratory Physiological Phenomena