Question

Oxygen-rich blood bound for the body tissues leaves the heart through the aorta, the major blood vessel emerging from the heart. It branches out to the arteries, which in turn branch into smaller vessels called arterioles (little arteries). These then branch into tiny, thin-walled capillaries. Blood travels slowly as the red blood cells squeeze through tiny capillaries. The radius of the aorta is approximately 9.8 mm and the speed of the blood there is 30 cm/s. A typical capillary has a diameter of approximately 6 µm. The flow speed in these capillaries is approximately 0.05 cm/s.

a. Draw a diagram of the blood vessels and indicate on the diagram the comparative flow speeds in these different-sized blood vessels. Discuss the direction and speed expected for the flow and the continuity equation for this system.

b. Using the given data, calculate how many capillaries a typical person would have.

c. What is the relationship between the combined cross-sectional area of the capillaries and the cross-sectional area of the aorta?

Answer #1

**Let
R1 = 9.8 mm = 0.0098 m
v1 = 30 cm/s = 0.3 m/s**

**d2 = 6 micro m = 6*10^-6 m
v2 = 0.05 cm/s = 5*10^-4 m/s**

**a)**

**b) Let N is the number of capallaries that a typical
person would have**

**use continuty equation,**

**A1*v1 = A2*v2**

**(pi*R1^2)*v1 = N*(pi*d2^2/4)*v2**

**==> N = 4*v1/(d2^2*v2)**

**= 4*0.3/((6*10^-6)^2*5*10^-4)**

**= 6.67*10^13
<<<<<<<--------------Answer**

**c) combined cross sectional area of the capaillaries, A2
= N*(pi*d2^2/4)**

**= 6.67*10^13*(pi*(6*10^-6)^2/4)**

**= 1886 m^2**

**cross sectional area of the aorta, A1 =
pi*R1^2**

**= pi*(9.8*10^-3)^2**

**= 3.02*10^-4 m^2**

**so, the combined cross-sectional area of the capillaries
= (1886/(3.02*10^-4))* the cross-sectional area of the
aorta**

**= 6.24*10^6*the cross-sectional area of the aorta
<<<<<<--------Answer**

The heart
pumps blood into the aorta at a rate of 4 L/min. Calculate the
average speed of blood if the aorta’s diameter is 2 cm.
The aorta branches many times until the blood finally reaches
the smallest branch: the capillaries. Each capillary has an average
diameter of 6 μm and a length of 1 mm, and the blood slows down to
0.5 mm/s. Calculate the number of capillaries in the body.

The radius of the aorta is about 1.0 cm , and the blood passing
through it has a speed of about 40 cm/s
Calculate the average speed of blood flow in the major arteries
of the body, which have a total cross-sectional area of about 2.2
cm2 .

The human circulatory system delivers oxygenated blood from the
lungs throughout the human body to enable the transport to and from
body cells of oxygen, carbon dioxide, nutrients, hormones and blood
cells. A variety of sizes of arteries and veins are required to
ful?l this need.
(a) A typical heartbeat pumps 75 mL of blood over a time span of
0.36 seconds into the aorta. If under this pressure the aorta
expands to a diameter of 4.2 mm, what is...

Use the data describing blood flow in the circulatory system
from the table below, and assume a typical blood flow rate of 5.0 L
per minute.
Aorta
Arteries
Arterioles
Capillaries
Venules
Veins
Vena cava
Diameter (cm)
2
0.5
0.002
0.0009
0.003
0.5
3
Total area (cm2)
3
20
500
4000
3000
80
7
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Express your answer with the appropriate units.
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(C) During sympathetic activation, the elastic arteries generate
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2. The chamber of the heart that sends blood to the
systemic circulation is the
a. left atrium b.
right ventricle ...

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