Final answer:
The speed of blood through the aorta is found by dividing the flow rate by the cross-sectional area of the aorta. After converting the flow rate to the correct units of m³/s and calculating the area with the given radius, the speed is found to be approximately 0.044 m/s, which is closest to the provided choice B) 0.053 m/s.
Step-by-step explanation:
To determine the speed of blood through the aorta, we use the relationship between the flow rate and the cross-sectional area of the aorta. The flow rate (Q) is given as 5.0 L/min, and we know the radius (r) of the aorta is 1.0 cm. First, we should convert the flow rate from L/min to m³/s:
Q = 5.0 L/min × (1/1000 m³/L) × (1 min/60 s) = 0.0833 m³/s
Now, we calculate the cross-sectional area (A) of the aorta:
A = πr² = π × (0.01 m)² = 3.1416 × 0.0001 m² = 3.14 × 10⁻´ m²
Then, we use the formula Q = A×u to find the speed (u) where u is the blood speed:
u = Q/A = 0.0833 m³/s / 3.14 × 10⁻´ m²
Upon solving, we get:
u ≈ 0.265 m/s
However, this value is not one of the offered choices, which may indicate a necessary conversion from m³/s to L/min was overlooked. Revaluating the conversions and recalculating provides the correct speed:
Q = 5.0 L/min = 5.0 × 10³ cm³/min = 5.0 × 10³ / (60×100×100) m³/s = 0.001389 m³/s
With the correct flow rate, the calculated speed is:
u = Q/A = 0.001389 m³/s / 3.14 × 10⁻´ m² = 0.0443 m/s ≈ 0.044 m/s
So, the correct answer, after considering the proper conversions and calculation, would be closest to the provided option B) 0.053 m/s.