Final answer:
The speed of the blood flow through a 2.00×10⁻⁶-m-radius capillary, given a flow rate of 3.80×10⁻⁹ cm³/s, is approximately 3.02×10⁻⁴ m/s.
So the correct option is;
Simplifying the equation, we find v ≈ 1.50 × 10-4 m/s.
Step-by-step explanation:
To calculate the speed of the blood flow through a capillary, we use the relationship which equates flow rate (Q) to the cross-sectional area (A) times the speed (v), which can be written as Q = A * v. Given that the flow rate (Q) is 3.80 × 10-9 cm³/s and must be converted to m³/s (1 cm³ = 1 × 10-6 m³), we get Q = 3.80 × 10-15 m³/s.
The cross-sectional area (A) of a capillary can be calculated using the formula for the area of a circle, A = π * r2, where the radius (r) is 2.00 × 10-6 m. Therefore, A = π * (2.00 × 10-6 m)2 = 1.256 × 10-11 m². The blood flow speed (v) is then found by dividing the flow rate (Q) by the area (A); v = Q / A = (3.80 × 10-15 m³/s) / (1.256 × 10-11 m²) ≈ 3.02 × 10-4 m/s.
To find the speed of the blood flow, we can use the equation v = Q/A, where v is the speed, Q is the flow rate, and A is the cross-sectional area of the capillary.
The radius of the capillary is given as 2.00×10-6 m, so the cross-sectional area can be calculated as A = πr2. Substituting the given values, we have A = π(2.00×10-6)2 and Q = 3.80×10-9 cm³/s. Plugging these values into the equation, we get:
v = 3.80×10-9 cm³/s / (π(2.00×10-6)2)
Simplifying the equation, we find v ≈ 1.50 × 10-4 m/s.