Question

(a) What is the largest average velocity of blood flow in an artery of radius $2\times {10}^{–3}$ m if the flow must remain laminar? (b) What is the corresponding flow rate? (Take viscosity of blood to be $2.084\times {10}^{–3}$ Pa s).

Answer 1

(a) Radius of the artery, $r=2\times {10}^{-3}m$
Diameter of the artery, $d=2\times 2\times {10}^{-3}m=4\times {10}^{-3}m$
Viscosity of blood, $\eta =2.084\times {10}^{-3}PaS$
Density of blood, $\rho =1.06\times {10}^{3}kg/m^3$
Reynolds’ number for laminar flow, $N_R=2000$
The largest average velocity of blood is given by the relation:
$V_{avg}=\frac{N_R\eta }{\rho d}$
$=\frac{2000\times 2.084\times {10}^{-3}}{1.06\times {10}^3\times 4\times {10}^{-3}}$
=0.983 m/s
Therefore, the largest average velocity of blood is 0.983 m/s.
(b) Flow rate is given by the relation:
$R=\pi r^2{V}_{avg}=3.14\times (2\times {10}^{-3}{)}^2\times 0.983=1.235\times {10}^{-5}{m}^3{s}^{-1}$
Therefore, the corresponding flow rate is $1.235\times {10}^{-5}{m}^3{s}^{-1}.$