When you are resting, your heart typically pumps about 5 L of blood through your

Question

When you are resting, your heart typically pumps about 5 L of blood through your body every minute. Your aorta has a radius of about 0.9 cm. What is the speed of blood flow in your aorta Your lungs are designed with tremendous redundancy; they have far more capillaries than are actually used at any one time. (The remaining capillaries are collapsed and do not support blood flow.) Each of your 300 million alveoli is surrounded by an estimated 1000 tiny capillaries. Each capillary has a radius of approximately 4 x10^4 cm, and blood flows in a capillary at a speed of about 5 x 10^4 m/s. Estimate the fraction of capillaries in your lung that are actually being used

Explanation / Answer

Part A

velocity of blood

v = flow rate/area

flow rate = 5L = 5*10^-3m^3/min = 5*10^-3/60 m^3/s

v = 5*10^-3 / pi*0.9*0.9*10^-4 * 60

v = 0.3276m/s

Part B

Now A1V1 = n(A2V2)

n = number of capillaries)

pi*0.9*0.9*10^-4 * 0.3276= n(pi*4*4*10^-8 *5*10^-4 )

n = 331695 capillaries

total number of capillaries

N = 300*10^6 *1000

N = 3*10^11

so fraction of capillary used = n/N = 331695/3*10^11

fraction = 1.105*10^-6

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