Question

(a) What is the largest average velocity of blood flow in an artery of radius 2 x 10^-3 m if the flow must remain laminar?

(b) What is the corresponding flow rate? (Take viscosity of blood to be 2.084 x 10^-3 Pa s). [Density of blood = 1.06 Kg m^-3]

Answer 1

Here,

r = 2 x 10^-3 m

η = 2.084 x 10^-3 Pa s

Taking the minimum value of Reynold's number for stream-line flow as;

N_R = 200

The maximum velocity is,

v_c = {N_Rη}/{ρd} = {N_Rη}/{2ρr} 

= {2000 x 2.084 x 10^-3}/{2 x 1060 x 2 x 10^-3}

= 0.98 ms^-1

Also, the rate of flow is:

V = av_c

= 3.143 x (2 x 10^-3)² x 9.8

= 1.24 x 10^-5 m³ s^-1