Answer:
To determine the factor by which the average velocity of the blood is reduced when it passes into the branches, we can use the principle of conservation of mass.
According to the principle of conservation of mass, the total mass flow rate of blood entering the major artery should be equal to the total mass flow rate of blood exiting the smaller arteries. Since blood is an incompressible fluid, the mass flow rate is directly proportional to the product of the cross-sectional area and the velocity of the blood.
Let's denote the average velocity of the blood in the major artery as V1 and the average velocity of the blood in the smaller arteries as V2. The cross-sectional area of the major artery is 1.0 cm^2, and the cross-sectional area of each smaller artery is 0.4 cm^2. Since the mass flow rate is conserved, we can write:
V1 * A1 = V2 * A2
where A1 is the cross-sectional area of the major artery and A2 is the total cross-sectional area of the smaller arteries.
The total cross-sectional area of the smaller arteries can be calculated by multiplying the average cross-sectional area of each smaller artery (0.4 cm^2) by the number of smaller arteries (18):
A2 = 0.4 cm^2 * 18 = 7.2 cm^2
Substituting the values into the equation, we have:
V1 * 1.0 cm^2 = V2 * 7.2 cm^2
Now, we can solve for the factor by which the average velocity is reduced:
V2 = (V1 * 1.0 cm^2) / (7.2 cm^2)
The factor by which the average velocity of the blood is reduced when it passes into the branches is given by V2/V1:
Factor = V2 / V1 = [(V1 * 1.0 cm^2) / (7.2 cm^2)] / V1
Simplifying the expression, we get:
Factor = 1.0 cm^2 / 7.2 cm^2
Therefore, the average velocity of the blood is reduced by a factor of approximately 0.139 (or 13.9%) when it passes into the branches.