4. The volume flow rate of blood leaving the heart to circulate throughout the b

Question

4. The volume flow rate of blood leaving the heart to circulate throughout the body is about 5 L/min for a person at rest. All this blood eventually must pass through the smallest of blood vessels, the capillaries. A typical capillary is 6 m (micrometer) in diameter, 1 mm long, and the blood flows through it at an average speed of 1 mm/s.

a. Estimate the total number of capillaries in the body. b. Estimate the total surface area of all the capillaries. (hint: the surface area of one capillary is A = circumference x length).

Explanation / Answer

Let there be n capillaries in our body.

volume flow rate of blood leaving the heart = 5 L/min
volume flow rate of blood leaving the heart = 8.33 * 10^-5 m^3/s

Area of capillary = 3.14 * 1/4 * (6*10^-6)^2 m^2
A = 2.826 * 10^-11 m^2
Velocity = 1 * 10^-3 m/s

Volumetric Flow rate = V*A
Volumetric Flow rate =  1 * 10^-3 * 2.826 * 10^-11 m^3/s
Volumetric Flow rate = 2.826 * 10^-14 m^3/s

As the Volumertic Flow remains Constant
8.33 * 10^-5  m^3/s = n * 2.826 * 10^-14
n = 2.95 * 10^9

Total surface area of all the capillaries = n * circumference x length
Total surface area of all the capillaries = 2.95 * 10^9 * 2*pi * (6*10^-6)/2 * 1 * 10^-3 m^2
Total surface area of all the capillaries = 55.6 m^2

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.