We will use a tube model for the circulatory system of an average man. This is a

Question

We will use a tube model for the circulatory system of an average man. This is a very simplistic picture but a nice starting point. Blood flows at a faster speed through the major arteries (about 4.7 cm/s) than through the capillaries (about 3.0 times 10^-2 cm/s). a) If we consider the total cross sectional area of the capillaries and arteries as if they were each made of one tube, what is the ratio of the artery areas to the capillary areas? b) The speed of the blood in the aorta is about 30 cm/s. The radius of the aorta is 1.0 cm, what is the combined area of the arteries? c) What is the combined area of the capillaries? d) The average cross-sectional area of an artery is 0.50 cm^2, how many arteries are in the body?

Explanation / Answer

(A) volume flow rate = constant

A v = constant

A_artery / A_capillary = v_capillary / v_artery

= 3 x 10^-2 / 4.7

=6.38 x 10^-3

(B) volume flow rate = (30 cm/s) (pi 1^2) = 30pi cm^3 / s

for arteries,

30 pi = (4.7) (A)

A = 20.05 cm^2

(C) 30 pi = (3 x 10^-2) (A)

A = 3141.6 cm^2

(D) n = (20.05) / (0.5)

n= 40

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