The aorta (the main blood vessel coming out of the heart) has a radius of about

Question

The aorta (the main blood vessel coming out of the heart) has a radius
of about 1.0 cm and the total cross section of the major arteries is about
20 cm^2. The density of blood is about the same as water, 1 g/cm^3.

a. Given that the velocity of blood pumping through the aorta is about 30 cm/s, what is the total current of the blood passing through the aorta (in mass of blood per second)?

b. If all the blood that flows through the aorta then branches into the major arteries, what is the velocity of blood in the major arteries?

c. The blood flowing in the major arteries then branches into the capillaries. If the velocity of blood in
the capillaries is measured to be 0.03 cm/s, what is the cross sectional area of the capillary system?

Explanation / Answer

a) mass of blood per second = density * velocity of blood * area = 1 * 30 * = 92.4 g/s

b) assuming density of blood is constant then from mass conservation of blood

Velocity of blood in arota * area of arota = vel of blood in major aritries * area of major artires

this gives

V = (30*)/ 20 = 4.71 cm/s

c) here also similar to above method

4.71 * 20 = 0.03 * area

this implies area = 3141 cm2

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