Answer to Question #278512 in Astronomy | Astrophysics for Lisa

Question

 The blood flows from the aorta of radius 1.0 cm to the millions of capillaries whose total cross section is 0.07 m2. The average speed of the blood flowing in these capillaries is 9 x 10－4 m/s. Calculate the speed flowing through the aorta. 

Answer 1

The flow of water is the same in all the capillaries and the aorta:

$$v_AA_A=v_cA_c,\\\space\\ v_A\pi r_A^2=v_cA_c,\\\space\\ v_A=v_c\frac{A_c}{\pi r_A^2}=0.2\text{ m/s}.$$