To determine the speed of blood through the aorta, we can use the equation for flow rate through a pipe:
Q = A * v
Where:
Q = Flow rate (volume per unit time)
A = Cross-sectional area of the aorta
v = Speed of blood through the aorta
We are given:
Flow rate, Q = 5.0 L/min = 5.0 * 10^-3 m^3/min
Radius of the aorta, r = 1.0 cm = 0.01 m
Area of the aorta, A = π * r^2
Density of blood, ρ = 1060 kg/m^3 (approximately)
Kinematic viscosity of blood, ν = 3.5 x 10^-6 m^2/s (approximately)
First, calculate the cross-sectional area of the aorta:
A = π * (0.01 m)^2
A = π * 0.0001 m^2
A = 3.14159 * 0.0001 m^2
A ≈ 3.14159 * 10^-4 m^2
Now, rearrange the formula Q = A * v to solve for v:
v = Q / A
v = (5.0 * 10^-3 m^3/min) / (3.14159 * 10^-4 m^2)
v = 15.9155 m/min
To convert the speed to meters per second, multiply by 1 min / 60 s:
v = 15.9155 m/min * (1 min / 60 s)
v ≈ 0.2653 m/s
Therefore, the speed of blood through the aorta is approximately 0.2653 m/s.