Final answer:
To find the equivalent diameter of a single vessel with the same cross-sectional area as the capillaries, one must apply the principle of flow rate (Q = A×v) and the formula for the area of a circle. However, without specific numerical data on the total cross-sectional area of the capillaries or the system's flow rate and velocity, determining the correct answer is not possible.
Step-by-step explanation:
The human cardiovascular system includes large vessels, like the aorta, and very small vessels, known as capillaries. Blood flows from the heart through the aorta and then branches into a vast network of capillaries, which have a much greater total cross-sectional area. This setup allows for an essential reduction in blood velocity, facilitating the exchange of substances with the cells. Considering the principles of flow rate (Q), we know that Q = A×v (where Q is the flow rate, A is the cross-sectional area, and v is the velocity). If the velocity in the aorta is considerably higher than in the capillaries, the total cross-sectional area of capillaries must be larger to maintain the same flow rate.
Since the question is asking for the equivalent diameter of a single vessel that would have the same cross-sectional area as the total area of the capillaries, we can use the formula for the area of a circle, A = π×r^2, where r is the radius. Rearranging the formula to solve for the diameter (d = 2×r), we can find the equivalent diameter given the total cross-sectional area.
However, the exact value of the cross-sectional area of the capillaries or a single equivalent vessel is not provided in the question or the reference information. To answer the provided multiple choice question, one would need specific numerical data indicating the cross-sectional area of the capillaries or the flow rate and velocity in the specific system being considered. Without such information, it would not be possible to determine the correct answer to the question.