Assume that your circulatory system is structured in a purely hierarchical fashion:

heart -> aorta -> arteries -> arterioles -> capillaries -> venules -> veins -> vena cava

Thus all of the blood flow out of the heart enters the aorta, all of the flow out of the aorta enters the arteries, all of the flow out of the arteries enters the arterioles, etc. Since the number of arterioles is larger than the number of arteries, the flow through each arteriole will be smaller than through each artery, etc.

Assume that the viscosity of the blood is a constant of .04 Poise. Use the following table:

Vessel | Pressure Drop (mmHg) | Lumen Radius (mm) | Average Length (cm) |
---|---|---|---|

aorta | ? | 12.5 | 30 |

artery | 2 | 2 | ? |

arteriole | 60 | 0.015 | 1.4 |

capillary | 14 | 0.004 | .16 |

venule | 4 | 0.01 | .59 |

vein | 5 | 2.5 | ? |

vena cava | ? | 15 | 30 |

The lumen is the cross sectional opening of the blood vessel.

3-1. Compute your surface area from the formula

A = 0.202 m^{ 0.425} h^{ 0.725}

where m = your mass in kg and h = your height in m.

Don't worry about the units; this is an "empirical" equation. That is, it is "derived" from a fit to empirical data, and all necessary units can be considered to be contained in the coefficient in order to produce square meters.

3-2. Use the empirical formula

O = | 4 A | if A < 1.25 |

3.5 A + 0.625 | if A >= 1.25 |

to find your cardiac output in liters per minute, where A = the surface area from problem # 3-1.

3-3. Assuming that we have one aorta and 40 arteries, compute the pressure drop in the aorta and the length of the average artery.

3-4. Assuming one vena cava and 20 veins, repeat problem # 3 for them.

3-5. Compute the number of arterioles, capillaries and venules in your body.

3-6. Compute the average blood velocity for each type of vessel.

3-7. What have you ignored to do these problems? How else might you do them with fewer idealizations?

3-8. A hypertensive patient is prescribed a vasodilator, which the doctor hopes will lower his diastolic pressure from 115 to 80. What is the ratio of the dilated radius to the undilated radius of one of his blood vessels, assuming that all other variables stay the same? Note that most medications affecting blood pressure also affect flow; we will ignore that detail here.

3-9. A cardiac patient undergoes bypass surgery in which an artery is replaced by one which is 10 % larger in diameter. What is the percentage change in blood flow in the artery, assuming all other factors remain the same?

If you have stumbled on this page, and the equations look funny (or you just want to know where you are!), see the College Physics for Students of Biology and Chemistry home page.

©1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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