Suppose that the average diameter of the aorta is 1.1 cm. The flow through the a

Question

Suppose that the average diameter of the aorta is 1.1 cm. The flow through the aorta is nearly the entirety of the cardiac output.
A. If the cardiac output is 5 L/min, what is the

average flow through the aorta?

B. Suppose further that the cardiovascular system is nearly closed to fluid transfer. That is, that on a short-term basis the volume of the blood does not change. This means that ALL of the blood that leaves the heart goes through the arteries, and then capillaries, and then returns to the heart through the veins. Using the continu- ity equation, what is the flow through the aggregate capillaries?

C. If the average diameter of the capillary is 4 3 1024 cm, and flow through the capillary is 0.1 cm s21, how many capillaries are there?

Explanation / Answer

given average diameter of aorta, d = 1.1 cm

A. Cardiac output = 5 L/min

let flow speed through aorta = v

then volume flow rate through it = pid^2*v/4

so 5L/min = 5*10^-3 m^3/60 s = pi*(1.1*10^-2)^2*v/4

v = 0.8768 m/s

average flow, v = 0.8768 m/s

B. as all the blood flows through the cappilaries

from equation of continuity, cardiac output = flow through all cappilaries = 5 L / min

C. average cappilary diameter, d = 0.43*10^-4 cm

cappilary flow rate, v = 0.1 cm/s

so volume flow rate through one capillary = pid^2*v/4 = pi*(0.43*10^-6)^2*0.1*10^-2/4 = 1.45*10^-16 m^3/s

so toal number of cappilaries be n

then

5*10^-3 m^3 / 60 s = n*1.45*10^-16

n = 5.7384*10^-11

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