185k views
3 votes
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 The blood returns to the heart via the veins. The radius of the aorta is about 1.2 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 2.0 cm 2

User MetaEd
by
7.1k points

1 Answer

6 votes

Final answer:

Using the equation of continuity, the average speed of blood flow in the major arteries with a total cross-sectional area of about 2.0 cm² is calculated to be 90.4 cm/s.

Step-by-step explanation:

To calculate the average speed of blood flow in the major arteries of the body with a total cross-sectional area of about 2.0 cm2, we can use the principle of conservation of mass, which in the case of fluid dynamics is represented by the equation of continuity:

A1v1 = A2v2, where A is the cross-sectional area of the vessel and v is the velocity of the blood flow. Given that the radius of the aorta is about 1.2 cm, we can calculate its cross-sectional area (A1), assuming it to be a circle, using the formula for the area of a circle A = πr2, which gives us A1 = π3.14 * (1.2 cm)2 ≈ 4.52 cm2.

The blood velocity (v1) in the aorta is given as 40 cm/s. The total cross-sectional area (A2) of the major arteries is given as 2.0 cm2. Using the equation of continuity, we can then find the average speed of the blood in the major arteries (v2) by rearranging the equation to solve for v2:

v2 = (A1 * v1) / A2

= (4.52 cm2 * 40 cm/s) / 2.0 cm2

v2 = 90.4 cm/s

Therefore, the average speed of the blood in the major arteries is 90.4 cm/s.

User Forex
by
8.2k points