Q = flow rate = speed * area
43 pi R^2 = n * .066 pi r^2
The aorta carries blood away from the heart at a speed of about 43 cm/s and has a radius of approximately 1.1 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 0.066 cm/s, and the radius is about 5.5 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.
2 answers
Aa/Ac - area of the aorta/area of capillary
Va/Vc - velocity of blood from the aorta/velocity of blood from capillaries
ac - area of a single capillary
ra/rc - radius of aorta/radius of capillary
n - number of capillaries
AaVa = AcVc
AaVa = nacVc. Separate area
pi*ra^2*Va = n*pi*rc^2*Vc. Arrange to solve for n
N = (ra^2*Va)/(rc^2*Vc) = 2.6 * 10^9 capillaries
Va/Vc - velocity of blood from the aorta/velocity of blood from capillaries
ac - area of a single capillary
ra/rc - radius of aorta/radius of capillary
n - number of capillaries
AaVa = AcVc
AaVa = nacVc. Separate area
pi*ra^2*Va = n*pi*rc^2*Vc. Arrange to solve for n
N = (ra^2*Va)/(rc^2*Vc) = 2.6 * 10^9 capillaries
1 answer