Mathematics and Biology  

Model Breakdown Physical Conditions 

Math Awareness Month 1999 

Poiseuille's Law: Typical Parameter Values

Pressure Drop: The complete circulatory system has a mean pressure drop of approximately 100 mmHg. The arterioles comprise 40%-60% of this decrease. 

Viscosity: Blood plasma has a viscosity of about 0.012 P, but with the red blood cells, this rises to around 0.05 P. This depends on the hematocrit ratio (typically 45%), the percentage of total blood volume composed of red blood cells. 

Radius: Typical diameters of arterioles are 30 micrometers (0.03 mm). The radius is half this value. However, these diameters are adjustable in order to quickly change the amount of blood that can flow. 

Length: An approximate length of a arteriole is 0.3-0.5 cm. 

For future comparisons, we will define our standard arteriole to match the following schematic: 
 
It will be 5 mm long, have a diameter of .03 mm, contain blood that has viscosity of 0.05 P (0.005 Pa s), and pressure difference of 50 mmHg (6650 Pa). Substituting these values into Poiseuille's law, we learn that in such an arteriole, the blood flows at the rate of 5.30E-6 cc/s (0.00000530 cubic centimeters per second). As an aid to visual understanding, the following graphic represents one second of blood flow. The growing parabola shows how far blood has advanced in the tube as a function of distance from the center. The spinning dial shows how much total blood volume has moved through the tube at the time. 


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D. Brian Walton is supported by a National Science Foundation Graduate Research Fellowship.