To determine the flow rate and the volume that passes through the artery in a period of 30 s, we can use the following formulas:
Flow rate (Q) = A * v
Volume (V) = Q * t
Where:
Q = Flow rate
A = Cross-sectional area of the artery
v = Speed of blood flow
V = Volume of blood flow
t = Time period (30 s)
Given:
Radius of the artery, r = 2 mm = 0.2 cm
Speed of blood flow, v = 40 cm/s
Time period, t = 30 s
First, calculate the cross-sectional area of the artery using the radius:
A = π * r^2
A = π * (0.2 cm)^2
A = π * 0.04 cm^2
A = 0.04π cm^2
Now, calculate the flow rate:
Q = A * v
Q = 0.04π cm^2 * 40 cm/s
Q = 1.6π cm^3/s
Next, calculate the volume that passes through the artery in 30 seconds:
V = Q * t
V = 1.6π cm^3/s * 30 s
V = 48π cm^3
Approximating π to be 3.14:
V ≈ 48 * 3.14 cm^3
V ≈ 150.72 cm^3
Therefore, the flow rate through the artery is approximately 1.6π cm^3/s and the volume that passes through the artery in a period of 30 s is approximately 150.72 cm^3.