   Chapter 9, Problem 81AP

Chapter
Section
Textbook Problem

The approximate diameter of the aorta is 0.50 cm; that of a capillary is 10. μm. The approximate average blood flow speed is 1.0 m/s ill the aorta and 1.0 cm/s in the capillaries. If all the blood in the aorta eventually flows through the capillaries, estimate the number of capillaries in the circulatory system.

To determine
The estimation of number of capillaries in the circulatory system.

Explanation
The cross-sectional area of aorta is Aaorta=(πdaorta2/4) and similarly for a single capillary of that is Acapillary=πdcapillary2/4 . It might be equal to the conservation of blood flow that is Aaorta=NAcapillary and the continuity of equation is presented for the calculation of number of capillaries in the circulatory system such that Nπdcapillary2vcapillary4=πdaorta2vaorta4N=(vaorta/vcapillary)(daorta/dcapillary)2 .

Given info: The approximate diameter of the aorta is 0.50cm , similarly the diameter of the capillary is 10μm , the approximate blood flow speed in aorta is 1.0m/s , and the blood flow speed in capillaries is 1.0cm/s .

The formula for the estimation of number of capillaries is,

• vaorta is approximate blood flow speed in aorta

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