## 5. The radius of the aorta is about 1.0 cm and blood passes through it at a velocity of 30 cm/s. A typical capillary has a radius of about 4 × 10–4 cm with blood passing through at a velocity of 5 × 10–2 cm/s. Using this data, what is the approximate number of capillaries in a human body?

A) 1 × 104

B) 2 × 107

C) 4 × 109

D) 7 × 1012

Rationale: This question asks you to recall the importance of fluids for the circulation of blood and to use modeling to make a prediction. Answering this question first requires you to recognize that the volume of blood flowing through the aorta is the same volume of blood flowing through the capillaries. You can use the continuity equation for fluids to reason that for a controlled volume, the sum of the flow rates in the capillaries must equal the flow rate in the aorta. Assume that the velocity of blood through each capillary tube, and their area, is the same.

This can yield the equation: Aaorta vaorta = n Acapillary vcapillary

In this equation, (A) is the area, (v) is the velocity, and (n) is the number of capillaries. Use the radii provided to calculate area (A = π r²) for the aorta and for a typical capillary; plug these numbers into the equation and solve for n, the approximate number of capillaries in the human body.