216 



SPEEDS OF SOME PROCESSES IN BIOLOGICAL SYSTEMS 



where p is the density of the flowing fluid, the fluidity, v the velocity of 

 flow, and r the tube radius. For homogeneous liquids flowing at constant 

 velocity, it is general experience that the flow is laminar and turbulence can- 

 not be maintained if Re < 2000. For blood, Re has been found to be 970 ± 

 80 over the pertinent range of flow rates and tube sizes. Therefore, laminar 

 flow probably occurs in the blood vessels at all times, although turbulence 

 may set in momentarily at the valves during the pumping action of the heart. 



Properties of Blood Plasma and Blood 



Previous discussion has implied that the fluidity (velocity per unit force 

 gradient) is independent of speed of flow, v. Liquids for which this is 

 true are called Newtonian liquids. Pure water is a good example. 



However, most real liquids are at least slightly "non-Newtonian" — that 

 is, = f(v). One of the most complex examples of this behavior is blood — 

 a suspension of cells in plasma, which itself is a water solution of salts and 

 heavily hydrated macromolecules. 



Figure 8-11 is taken from results which show that the ease of pushing the 

 fluid through a tube — in this case a glass one — decreases rapidly with intro- 

 duction of macromolecules and cells into water. Thus the for plasma is 



about half that for water [144 — /— — -); and increasing amounts of red 



\ sec/ cm / 



blood cells reduce the fluidity still further. Yet, to a first approximation, 



> blood 



AP 



Figure 8-11. Rate of Flow of a Fluid Through a Tube as a Function of Driving Pressure. 

 The slope is proportional to the fluidity, given in parentheses. The usual range of per- 

 centage of total fluid volume filled with cells is shaded in. 



