Question

In the human circulatory system, the blood flows out of the heart via the (single) aorta which is connected to other arteries which branch out into a number of smaller arteries and then to a large multitude of small capillaries. In the average adult, the aorta has a cross-sectional area of 2.5 cm², the net cross sectional area of all of the numerous small arteries when added up is 20 cm², and the net area of of the 10 billion capillaries when added up is 2500 cm². Neglecting viscosity and assuming incompressible flow, where is the blood velocity the smallest?

a. The flow velocity is the same in all of these.
b. The small (but not timy) less numerous arteries.
c. The single aorta.
d. The tiny but incredibly numerous capillaries.

Answer 1

The smallest blood velocity occurs in the capillaries, where the combined cross-sectional area is the largest, slowing down the flow to enable efficient exchange of substances with cells.

Step-by-step explanation:

The blood velocity is the smallest in the tiny but incredibly numerous capillaries. Given the provided cross-sectional areas, we can deduce this by applying the principle of continuity in fluid dynamics. This principle states that in the absence of viscosity, the product of cross-sectional area (A) and flow velocity (v), or the flow rate (Q), is constant (Q = Av). Thus, when blood moves from the single aorta with a smaller cross-sectional area to the capillaries with a much larger combined cross-sectional area, the velocity must decrease to maintain a constant flow rate.

When the cross-sectional area increases due to the branching of blood vessels, the average velocity of the blood decreases to compensate. As the aorta branches into arteries and then to capillaries, it is the massive total cross-sectional area of the capillaries compared to that in the aorta that results in slower blood flow in the capillaries. The decreased velocity is crucial for efficient exchange of oxygen, nutrients, and waste products between the blood and the cells.