The human heart is a mechanical pump. The aorta is a large artery that carries oxygenated blood away

from the heart to various organs in the body. For an individual at rest, the blood in the aorta (of radius
1.25 cm) flows at a rate of 5*103 cm3/min (5 liter/min). What is the velocity, in meters per second, of the
blood in the aorta?
a. 0.17 m/s
b. 1.02 m/s
c. 0.533 m/s
d. 6.6*10-3 m/s
e. 2.12*10-3 m/s

a. 0.17 m/s

To find the velocity of the blood in the aorta, we can use the equation for the flow rate of a fluid through a pipe:

Q = A * v

where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the fluid.

Given that the flow rate is 5*10^3 cm^3/min, we need to convert it to m^3/s:

Q = (5*10^3 cm^3/min) * (1 m^3 / 10^6 cm^3) * (1 min / 60 s)
Q = (5*10^-3 m^3/s)

The radius of the aorta is 1.25 cm, so the cross-sectional area can be calculated using the formula:

A = π * r^2

A = π * (1.25 cm)^2 * (1 m^2 / 10^4 cm^2)
A = π * (1.25*10^-2 m)^2
A = π * (1.5625*10^-4 m^2)
A = 4.91*10^-4 m^2

Now we can rearrange the flow rate equation to solve for velocity:

v = Q / A
v = (5*10^-3 m^3/s) / (4.91*10^-4 m^2)
v = (5/4.91) m/s
v ≈ 1.02 m/s

Therefore, the velocity of the blood in the aorta is approximately 1.02 m/s. Therefore, the answer is b. 1.02 m/s.

To find the velocity of blood in the aorta, we can use the equation for the flow rate of a fluid through a pipe, which is given by:

Flow rate = (Velocity) * (Cross-sectional Area)

In this case, the flow rate is given as 5 * 10^3 cm^3/min, which is equivalent to 5 liters/min.

First, we need to convert the flow rate to SI units. Since 1 liter is equal to 1000 cm^3, we have:

Flow rate = (5 * 10^3 cm^3/min) * (1 liter/1000 cm^3) * (1 min/60 s)
Flow rate = 83.33 cm^3/s

Next, we need to calculate the cross-sectional area of the aorta. The formula for the area of a circle is given by:

Area = π * (Radius)^2

Using the given radius of 1.25 cm, we have:

Area = π * (1.25 cm)^2
Area = 4.91 cm^2

Now, we can rearrange the equation for flow rate to solve for velocity:

Velocity = Flow rate / Cross-sectional Area

Substituting the values we calculated, we get:

Velocity = 83.33 cm^3/s / 4.91 cm^2
Velocity ≈ 17 cm/s

Finally, we need to convert the velocity to meters per second. Since 1 cm is equal to 0.01 m, we have:

Velocity = 17 cm/s * (0.01 m/cm)
Velocity ≈ 0.17 m/s

Therefore, the velocity of blood in the aorta is approximately 0.17 m/s. The correct answer is option a. 0.17 m/s.