Answer:
The average blood speed is 0.39 m/s
Step-by-step explanation:
According to Poiseuille’s law, the volume flow rate, Q (m³/s) of a fluid of
viscosity η through a tube or pipe of radius r and length L is:
Q = πr⁴ΔP/8ηL
where ΔP is the change in pressure or pressure difference of the fluid; L is length of the pipe
Also, the volume flow rate, Q, is related to the average velocity v, by the formula:
Q = Av
where A is the cross-sectional area of the pipe; A = πr²
Q = πr²v
Thus, the Poiseuille’s becomes: πr²v = πr⁴ΔP/8ηL
v = r²ΔP/8ηL
From the given values:
r = 2.5 mm = 0.0025 m
L = 15 cm = 0.15 m
ΔP = 380 Pa
η = 5 * 10⁻³ Pa.s
substituting the given values in the equation
v = {(0.0025)² * 380} / (8 * 5 * 10⁻³ * 0.15)
v = 0.39 m/s
Therefore, the average blood speed is 0.39 m/s