Velocity Profiles for Blood: The constitutive relation for the flow of blood in a cylindrical tube of

radius $R$ is

$|{}_{rz}|>{}_0,({}_{rZ}{)}^{\frac{1}{2}}=({}_0{)}^{\frac{1}{2}}+({}_N{)}^{\frac{1}{2}}(\frac{d{v}_z}{dr}{)}^{\frac{1}{2}}$

And

$|{}_{rz}|{}_0,\frac{d{v}_z}{dr}=0$

Where ${}_0$ is the yield stress and ${}_{}$ is the Newtonian viscosity at high shear rates.

$($a$)$ Show that the velocity profile is:

$r_c=\frac{{}_{0}2L}{p}\frac{{}_w}{{}_0}=\frac{R}{r_c}(p\frac{R^2}{4}{}_{N}L)\frac{r}{R}\frac{{}_w}{{}_0}0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1,0\mathrm{.}2{}_w^2{}_{w}c{m}^{-2}$