Answer to Question #270292 in Physics for Grazi

Question

In an adult, the aorta's radius is normally ~1.5cm, and blood moves through it at an average speed of 30m/s. If a typical capillary has a radius of 5×10^-6m and blood passes through them with velocity of 0.1cm/s approximately how many capillaries are in the blood?

Answer 1

The volumetric flows that pass through the aorta and capillaries are equal:

$$A_1v_1=A_2v_2\equiv\text{const}.\\\space\\ A_a=\pi R^2,A_c=\pi r^2,\\\space\\ A_av_a=NA_cv_c,\\\space\\ N=\frac{A_av_a}{A_cv_c}=\frac{R^2v_a}{r^2v_c},\\\space\\ N=\frac{0.015^2·30}{(5·10^{-6})^2·0.001}=2.7·10^{11}.$$