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 lanimar? (b) What is the corresponding flow rate ? (Take viscosity of blood to be $2.084\times {10}^{-3}Pas$).

Answer 1

(a) Radius of the artery $r=2\times {10}^{-3}m$

Diameter, $D=2\times 2\times {10}^{-3}m=4\times {10}^{-3}m$

Viscosity of the blood $\eta =2.084\times {10}^{3}Pa$

Density of the blood $\rho =1.06\times {10}^{3}kg{m}^{-3}$

Maximum valu of Reynold number of flow to be laminar, $N_R=20N$

Average velocity $V_c=\frac{N_R\eta }{\rho D}$

$=\frac{2000\times 2.084\times {10}^3}{1.06\times {10}^3\times 4\times {10}^3}$

$=\frac{4.168}{4.24}=0.98m/s$

(b) Flow rate is given by the relation:
$R=\pi r^{2}V\left(avg\right)$
$=3.14\times (2\times {10}^{-3}{)}^2\times 0.983$
$=1.235\times {10}^{-5}{m}^3/s$
Therefore, the corresponding flow rate is $1.235\times {10}^{-5}{m}^3/s.$