$(a)$ 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 $2.084 \times 10^{-3} \; Pa \; s$).

(N/A) Radius of the artery,$r = 2 \times 10^{-3} \; m$
Diameter of the artery,$d = 2r = 4 \times 10^{-3} \; m$
Viscosity of blood,$\eta = 2.084 \times 10^{-3} \; Pa \; s$
Density of blood,$\rho = 1.06 \times 10^{3} \; kg/m^{3}$
Reynolds' number for laminar flow,$N_{R} = 2000$
$(a)$ The largest average velocity $(V_{avg})$ is given by the relation:
$V_{avg} = \frac{N_{R} \eta}{\rho d}$
$V_{avg} = \frac{2000 \times 2.084 \times 10^{-3}}{1.06 \times 10^{3} \times 4 \times 10^{-3}}$
$V_{avg} \approx 0.983 \; m/s$
$(b)$ The flow rate $(Q)$ is given by:
$Q = A \times V_{avg} = \pi r^{2} V_{avg}$
$Q = 3.14 \times (2 \times 10^{-3})^{2} \times 0.983$
$Q \approx 1.235 \times 10^{-5} \; m^{3}/s$