Final answer:
The average speed of blood flow in the major arteries, assuming a total cross-sectional area of about 2.1 cm², is calculated using the continuity equation and is approximately 52 cm/s.
Step-by-step explanation:
To calculate the average speed of blood flow in the major arteries of the body, we can use the principle of conservation of mass, commonly referred to as the continuity equation in fluids. The equation states that the flow rate must be constant throughout the circulatory system, which implies that the product of cross-sectional area and the speed of blood is constant. Given that the speed of blood in the aorta is 35 cm/s and its radius is 1.0 cm, we can first find the flow rate and then use it to find the average speed in the major arteries that have a total cross-sectional area of about 2.1 cm². The flow rate (Q) can be calculated using the formula Q = A * v, where A represents the cross-sectional area and v represents the speed. For the aorta, the cross-sectional area A is π * r² = 3.14 * (1 cm)² = 3.14 cm². Thus, the flow rate is Q = 3.14 cm² * 35 cm/s = 109.9 cm³/s. To find the average speed (v) in the major arteries, we rearrange the equation to v = Q / A. Therefore, v = 109.9 cm³/s / 2.1 cm² = 52.33 cm/s. To express our answer to two significant figures, we get 52 cm/s as the average speed of blood flow in the major arteries.