Problem $3$: Murray's law

$3$a: Using velocity profile for fully developed flow through a cylinder driven by a pressure gradient. Define the maximum velocity, flow rate, resistance, and wall shear stress. In relation to Murray's law, show how the shear stress remains constant when a large blood vessel bifurcates into $2$ smaller ones of equal radius.

$3$b: Calculate: wall shear rate, wall shear stress, and vascular resistance for the following $($assume viscosity $=0\mathrm{.}03$ poise$)$

$\backslash$table$[[$Blood Vessel,Diameter $($ cm $),\backslash$table$[[$Blood$],[$Velocity$],[($average$)],[(c\frac{m}{sec})]],\backslash$table$[[$Wall Shear$],[$Rate$]],\backslash$table$[[$Apparent$],[$Viscosity$],[($poise$)]],$Wall Shear stress,$\backslash$table$[[$Vascular$],[$Resistance $/],[$dyn:s$-$cm$^-5)]]],[$Aorta$,1,50,,,,],[$Large Arteries,$0\mathrm{.}3,13,,,,],[,0\mathrm{.}3,19,,,,],[,0\mathrm{.}34,23,,,,],[$Small arteries,$0\mathrm{.}1,8,,,,],[$Terminal Branches,$0\mathrm{.}06,6,,,,],[$Arteriole$,0\mathrm{.}002,0\mathrm{.}3,,,,]]$

$3$c: Plot shear stress versus diameter