Question

The aorta pumps blood away from the heart at about 40 cm/s and has a radius of about 1.0 cm. It then branches into many capillaries, each with a radius of about 5×10−4 cm carrying blood at a speed of 0.10 cm/s. How many capillaries are there?
a. 1.6×109
b. 16
c. 8.0×105
d. 1.6×105

Answer 1

Answer:

  a.  1.6×10^9

Step-by-step explanation:

The blood volume flowing per second is the same in each vessel, so we have ...

  $r_1^2v_1=n\cdot r_2^2v_2\\\\1^2\cdot 40=n\cdot (5\times 10^{-4})^2\cdot 0.1\\\\\dfrac{40}{2.5\times 10^{-8}}=n=1.6\times 10^9$

There are about 1.6×10^9 capillaries.