Question

The radius of the aorta is about 1.4 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 1.8 cm^2

Answer 1

This is an example of flow rate.
The aorta = narrow = I will use the subscript n to represent variables related to the aorta
The artery = wide = I will use the subscript w to represent variables related to the aorta

We use the flow rate equation:
A1 * V1 = A2 * V2 --> and now we relate it to the question --> An * Vn = Aw * Vw
A is area, and V is velocity

I first need to find the area of the aorta, as it only gives me 1.4 cm as a radius.
Convert 1.4 cm to m by dividing by 100 --> 1.4cm / 100 = 0.014m
Assuming the aorta is circular, we can find the area as (pi)r^2:
(pi)*(0.014m)^2 = approx. 6.154e-4m^2

To keep the units alike, I will now convert the area of the artery (1.8cm^2) to m^2:
1.8cm^2 = 1.8e-4m^2

Converting the velocity of blood in aorta from 40 cm/s to m/s --> 0.4 m/s
Now we plug the numbers in:

An * Vn = Aw * Vw
( 6.154e-4m^2) * (0.4 m/s) = (1.8e-4m^2 ) * Vw
2.4616e-4 m^3/s = (1.8e-4 m^2) * Vw
Vw = approx. 0.13675 m/s

The velocity of blood flow in the major arteries of the body is approximately 0.13675 m/s or 13.675 cm/s.