In the problem on the circulatory system, you looked at pressure differences bet
ID: 83090 • Letter: I
Question
In the problem on the circulatory system, you looked at pressure differences between various points. In some of these calculations, viscosity can be ignored as compared with the other factors that affect the pressure difference. Discuss under what circumstances that the viscosity of the blood may be ignored in computing pressure differences. Your discussion must include reasoning based on appropriate principles and your conclusions must be illustrated with appropriate calculations applied to a reasonable model. (For reference, the viscosity of blood is 4.0 times 10^-3 Pa middot s, and the density of blood is 1060 kg/m^3.)Explanation / Answer
All rheological and flow measurements within the microvasculature are subject to all the uncertainties associated with an impressive knowledge of the vascular geometry. When computing the effective viscosity of the blood from the measurements of pressure drop and flow it is assumed that the vessel is a smooth walled cylinder of circular cross section. During this calculation, the viscosity of the blood is neglected to get appropriate pressure differences.
Many venules appear to be elliptical in cross section and departure from the original is ignored when measuring the venular diameter from observations of the width of a venule in the focal plane of a living tissue. Measuring the in vivo apparent viscosity of blood in the microcirculation, it was found that the viscosity was 43% greater in venules compared to arterioles.
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