Question

The aorta carries blood away from the heart at a speed of about 42 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 0.064 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.

Answer 1

The number of capillaries is

`N=2.625x10^9` Capillaries

Step-by-step explanation:

`v_(aorta)=42cm/s`,
`r_(aorta)=1.1 cm`,
`v_(cap)=0.064cm/s`,
`r_(cap)=5.5x10^(4)cm`,

To find the number of capillaries in the human body use the equation:

`N_(cap)=(v_(aorta)*\pi*r_(aorta)^2)/(v_(cap)*\pi*r_(cap)^2)`

So replacing numeric

`N_(cap)=(42cm/s*\pi*(1.1cm)^2)/(0.064cm/s*\pi*(5.5x10^(-4)cm)^2)`

Now we can find the number of capillaries

`N=26250000000`

`N=2.625x10^9` Capillaries