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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 :

davidlcastiblanco

Answer:

The number of capillaries is

[tex]N=2.625x10^9[/tex] Capillaries

Explanation:

[tex]v_{aorta}=42cm/s[/tex], [tex]r_{aorta}=1.1 cm[/tex], [tex]v_{cap}=0.064cm/s[/tex], [tex]r_{cap}=5.5x10^{4}cm[/tex],

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

[tex]N_{cap}=\frac{v_{aorta}*\pi*r_{aorta}^2}{v_{cap}*\pi*r_{cap}^2}[/tex]

So replacing numeric

[tex]N_{cap}=\frac{42cm/s*\pi*(1.1cm)^2}{0.064cm/s*\pi*(5.5x10^{-4}cm)^2}[/tex]

Now we can find the number of capillaries

[tex]N=26250000000[/tex]

[tex]N=2.625x10^9[/tex] Capillaries

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