Final answer:
The flow velocity of the blood is reduced by a factor of approximately 1/7.2 when a major artery with a cross-sectional area of 1.00 cm² branches into 18 smaller arteries with a total cross-sectional area of 7.2 cm².
Step-by-step explanation:
When a major artery with a cross-sectional area of 1.00 cm² branches into 18 smaller arteries, each with an average cross-sectional area of 0.400 cm², the blood flow velocity decreases. This change is calculated based on the principle of conservation of mass which implies that the volume flow rate (Q) must be the same in the main artery and the branches, where Q = A⋅u (A is the cross-sectional area and u is the velocity).
To find by what factor the average velocity of the blood is reduced, we must realize that if the total cross-sectional area of the branches increases, the velocity decreases to maintain the same flow rate. The total cross-sectional area of the 18 smaller arteries is 18 × 0.400 cm² = 7.2 cm². Therefore, the flow velocity is reduced by a factor of 1.00 cm² / 7.2 cm² = 0.1389 (approximately 1/7.2).