The Speed of the Blood The aorta (the main blood vessel coming out of the heart)

Question

The Speed of the Blood

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 cm2. The density of blood is about the same as water, 1 g/cm3.

(a) Given that the velocity of blood pumping through the aorta is about 35 cm/s, what is the total current of the blood passing through the aorta (in mass of blood per second)?

____ g/s

(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?

____ cm/s

(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 0.05 cm/s, what is the cross sectional area of the capillary system?

____ cm2

Explanation / Answer

densiy of blood d = 1g/cm^3

ra = 1 cm , Am = 20cm^2

(a) va =35 cm/s

m = dV

m/t = d(V/t)

here V/t is volume flow rate = Aava

m/t = dAava = (1*3.14*1*1*35) =109.9 g/s

(b) Volume flow rate is constant

Aava =Amvm

vm=Aava/Am = [3.14*1*1*35]/(20)

vm = 5.495 cm/s

(c) vc = 0.05cm/s

Volume flow rate is constant

Aava =Amvm = Acvc

Ac=Aava/vc = [3.14*1*1*35]/(0.05)

Ac = 2198 cm2

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