The aorta carries blood away from the heart at a speed of about 40cm/s and has a

Question

The aorta carries blood away from the heart at a speed of about 40cm/s and has a radius of approximately 1.1 cm. The aorta brancheseventually into a large number of tiny capillaries that distributethe blood to the various body organs. In a capillary, the bloodspeed is approximately 0.07 cm/s, and the radius is about 6 x10-4 cm. Treat the blood as an incompressible fluid, anduse these data to determine the approximate number of capillariesin the human body.

Explanation / Answer

Suppose the aorta gets divided into N capillaries. According to the equation of continuity, the volume rate of flow through the aorta ahould be equal tothe total volume rate of flow through all the capillaries. So, Av = NA'v' A, A' -> areas of cross section of the aorta and thecapillaries v,v' -> speeds of flow through the aorta and thecapillaries. So, (r2)*v = N*(r'2)*v' So, N = (r/r')2*(v/v') =(11000/6)2*(40/0.07) = 1.921 billion capillaries

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