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
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
First, calculate the cross-sectional area of the aorta using the radius:
A = π * r^2
A = π * (0.01 m)^2
A = π * 0.0001 m^2
A = 0.0001π m^2
Now, use the formula Q = A * v to solve for the speed of blood through the aorta:
5.0 * 10^-3 m^3/min = 0.0001π m^2 * v
v = (5.0 * 10^-3 m^3/min) / (0.0001π m^2)
v = 0.05 / π m/min
To convert the speed to a more recognizable unit, such as cm/s, we can convert from m/min to cm/s:
v = (0.05 / π) m/min * (100 cm / 1 m) * (1 min / 60 s)
v ≈ 0.53 cm/s
Therefore, the speed of blood through the aorta is approximately 0.53 cm/s.