The aorta (the main blood vessel coming out of the heart) has a radius of about
ID: 1465820 • Letter: T
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 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 27 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 0.02 cm/s, what is the cross sectional area of the capillary system?
______ cm2
Explanation / Answer
a) Let v1 = 27 cm/s
cross sectional area of arota, A1 = pi*r^2
= pi*1^2
= 3.14 cm^2
mass flow rate = rho*A1*v1
= 1*3.14*27
= 84.8 g/s <<<<<<<<<------------Answer
b) Let A2 = 20 cm^2
Apply, continuty equation
A2*v2 = A1*v1
v2 = A1*v1/A2
= 3.14*27/20
= 4.24 cm/s <<<<<<<<<------------Answer
c) let V3 = 0.02 m/s
A3 = ?
Again use continuty equation
A3*V3 = A2*v2
A3 = A2*v2/V3
= 20*4.24/0.02
= 4240 cm^2 <<<<<<<<<------------Answer
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