An artery has an inner radius of 2.0 x 10^-3m. if the temperature is 37 degree celcius, the average velocity of the blood is 0.030ms^-1 and the flow is laminar flow. find (a)the maximum velocity, (b) the flow rate and (c) the pressure drop in 0.050m, if the artery is horizontal.
To solve this problem, we can use the equation for Poiseuille's Law, which relates the flow rate, pressure drop, and properties of the fluid and the vessel it flows through.
(a) The maximum velocity can be determined by dividing the average velocity by 0.5. In laminar flow, the velocity profile is parabolic, which means that the maximum velocity is twice the average velocity. So,
Maximum Velocity (v) = 2 x average velocity = 2 x 0.030 m/s = 0.060 m/s.
(b) The flow rate (Q) can be calculated using the formula:
Q = πr^2v,
where r is the radius of the artery and v is the average velocity of the blood.
Given:
r = 2.0 x 10^-3 m
v = 0.030 m/s
Plugging in the values:
Q = π(2.0 x 10^-3)^2(0.030) m³/s
Q ≈ 0.000001506 m³/s.
(c) The pressure drop (∆P) in 0.050 m can be determined by:
∆P = 8ηLQ / πr^4,
where η is the dynamic viscosity of blood and L is the length of the vessel.
Given:
η (dynamic viscosity of blood) is not provided.
L = 0.050 m
Q = 0.000001506 m³/s (calculated in part b)
r = 2.0 x 10^-3 m
To determine the pressure drop (∆P), we need the dynamic viscosity of blood (η). Unfortunately, the dynamic viscosity of blood is not provided in the question. Therefore, it is not possible to calculate the pressure drop (∆P) without this information.
Please note that in real-life applications, the dynamic viscosity of blood is usually known and can be obtained from medical literature or clinical data.