ON FLUID FLOW; BLOOD 215 



fluidity. Viscosity can be considered as the frictional force opposing the 



a x j- • dynes /cm . . , . . . . „ , , 



How. Its dimensions are — / , or dyne sec/cm , this unit is called the 



cm / sec 

 poise, after Poiseuille. 



A very simple way to measure fluidity or viscosity is in the Ostwald vis- 

 cometer. The capillary pipette is filled to a mark with fluid, and measure- 

 ment made of the time it takes the fluid to run out of the pipette. This time 

 is divided into the time taken by water, or some other fluid, to drain at the 

 same temperature. The quotient is called the relative viscosity. A density cor- 

 rection is necessary if the driving force (gravitational) is to be equal in the 

 two cases. 



Solutions or suspensions (of molecules or particles respectively) in water 

 usually increase the viscosity (decrease the fluidity). The fractional increase 

 is (r;, — ri )/rj , where the subscripts s and refer to solution and pure 

 water, respectively. But this value, often called 77', varies with the concentra- 

 tion. It is convenient, then, to measure the 77' at several concentrations, and 

 express each measurement in terms of unit concentration by dividing by the 

 concentration at which the measurement was made. This number is called 

 the specific viscosity. It is also concentration-dependent, because intermolec- 

 ular interactions are higher at higher concentrations. It is useful, then, to 

 extrapolate measurements of specific viscosity to infinite dilution (zero con- 

 centration), for this value is the value of that part of the viscosity due to the 

 suspension only, and unaffected by interactions which solute particles could 

 have on each other. This value is called intrinsic viscosity, usually symbolized 

 [77]. Values range from .02 for small- molecular- weight solutes to 20 for 

 macromolecules, and to much higher values for suspensions of living cells. 



Turbulent Flow 



Laminar flow will exist in most fluids at low rates of flow. When the flow 

 rate becomes high, the glide planes get off-track, and turbulence sets in. 

 Small whirlpools and eddy currents are initiated, and the fluidity drops 

 abruptly; therefore, if the rate of flow is to be maintained, higher driving 

 force must be applied and more energy must be expended. Unless some 

 result of particular value is derived from the turbulence (more rapid mixing 

 of chemical reactants at a reaction site, for example), it is obviously waste- 

 ful of energy. The circulatory system in man has certain features, such as 

 flexible walls lined with hydrated protein "hairs," which help direct the fluid 

 flow and damp out trends toward turbulence. 



The Reynolds number, Re, a dimensionless parameter of fluid flow, is 

 defined as 



Re = 20 p vr 



