Blood flows in a steady$-$state in a $3$ mm radius, $4$ cm long artery with a pressure gradient of $40$ Pa$/$m$.$ It has a yield shear stress of $0\mathrm{.}02$ dynes$/$cm$2$ and a viscosity of $3$ cP $[10$ marks$]$

a$)$ Calculate the region of critical radius, where plug flow occurs. $[3$ marks$]$

b$)$ Based on your calculation, can we assume Newtonian behaviour or not? $[2$ marks$]$

c$)$ c$)$ Calculate the flow rate Q in this artery based on your answer in b$).$ How would the flow change if the fluid was more non$-$Newtonian and how would you calculate it$?$