Final answer:
The single 4-mm blood vessel would carry more fluid than two 2-mm blood vessels because resistance is inversely proportional to the fourth power of the radius, making the larger vessel's resistance much lower.
Step-by-step explanation:
When considering the fluid flow through blood vessels with different diameters while keeping the pressure constant, we must take into account the concept of vessel diameter's influence on resistance and flow rate. The resistance to flow is inversely proportional to the fourth power of the vessel's radius (which is half of the diameter).
So, when comparing one 4-mm blood vessel to two 2-mm blood vessels, the single larger vessel would have a lower resistance and, therefore, potentially a higher flow rate, assuming all other factors are equal.
Moreover, the total cross-sectional area of two smaller vessels combined is greater than the area of a single vessel with the same total diameter. This increased total cross-sectional area can reduce resistance and might suggest that more fluid could be carried by two 2-mm vessels.
However, due to the exponential impact of the radius on resistance, the single larger vessel still offers less resistance overall. The reason for this is that even though two 2-mm vessels have a larger combined cross-sectional area, their smaller individual radii significantly increase the resistance, which reduces flow.