Assume that the average human aorta has a radius of 1 cm. The blood flow rate is approximately 84 cm3/s . What is the velocity of blood flow in cm/s?
Question
Assume that the average human aorta has a radius of 1 cm. The blood flow rate is approximately 84 cm3/s . What is the velocity of blood flow in cm/s?
Solution
To find the velocity of the blood flow, we can use the formula for the flow rate, which is Q = vA, where Q is the flow rate, v is the velocity, and A is the cross-sectional area of the flow.
Step 1: Calculate the cross-sectional area (A) of the aorta using the formula for the area of a circle, A = πr², where r is the radius of the aorta. Given that the radius of the aorta is 1 cm, the area would be A = π(1 cm)² = π cm².
Step 2: Rearrange the flow rate formula to solve for velocity, v = Q/A.
Step 3: Substitute the given flow rate (Q = 84 cm³/s) and the calculated area (A = π cm²) into the formula.
v = 84 cm³/s / π cm² = 84/π cm/s ≈ 26.7 cm/s.
So, the velocity of the blood flow in the aorta is approximately 26.7 cm/s.
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