In humans, blood flows from the heart into the aorta, from which it passes into
ID: 1463117 • Letter: I
Question
In humans, blood flows from the heart into the aorta, from which it passes into the major arteries. These branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries, see the figure. The blood returns to the heart via the veins. The radius of the aorta is 1.0 cm and the blood passing through it has a speed of about 28 cm/s. A typical capillary has a radius of about 4 × 10-4 cm, and blood flows through it at a speed of about 5 × 10-4 m/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 cm2.
Explanation / Answer
We can use the flow rate equation:
A1 * V1 = A2 * V2 --> and now we relate it to the question, 1 is aorta , 2 is arteries (notation)
A is area, and V is velocity
Radius of aorta is 1.0cm / 100 = 0.01m
Assuming the aorta is circular, we can find the area as (pi)r^2:
(pi)*(0.01m)^2 = approx. 3.14 e-4m^2
convert the area of the artery (2.2cm^2) to m^2:
1.8cm^2 = 1.8e-4m^2
Converting the velocity of blood in aorta from 28 cm/s = 0.28 m/s
Substituting all the above
A1 * V1 = A2 * V2
(3.14e-4 m^2) * (0.4 m/s) = (1.8e-4 m^2) * V2
V2 = 0.697 m/s
Hence , The velocity of blood flow in the major arteries of the body is approximately 0.697 m/s