The aorta carries blood away from the heart at a speed of about 41 cm/s and has

Question

The aorta carries blood away from the heart at a speed of about 41 cm/s and has a radius of approximately 1.0 cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approximately 0.062 cm/s, and the radius is about 6.2 x 10-4 cm. Treat the blood as an incompressible fluid, and use these data to determine the approximate number of capillaries in the human body. (Hint:calculate the volume flow rate in the aorta, and in each capillary. Divide to find the number of capillaries.)

Explanation / Answer

Flow rate = Cross sectional area * speed Blood flow from the aorta = (pi)(1)^2(41) = 128.74 cm^3/sec. Blood flow rate from the aorta to the capillaries is CONSTANT. Thus being said, 128.74 = (pi)(0.00062)^2(0.062)(N) where N = number of capillaries Solving for "N", N = 1.72billion (approximately)

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