Problem $1.$ A power$-$law biological fluid, banana puree, is flowing at $23\mathrm{.}9C,$ with a velocity of

$1\mathrm{.}018\frac{m}{s},$ through a smooth tube $6\mathrm{.}10m$ long having an inside diameter of $0\mathrm{.}01267m.$ The flow

properties of the fluid are $K=6\mathrm{.}00N*\frac{s^{0\mathrm{.}454}}{m^2}$ and $n=0\mathrm{.}454.$ The density of the fluid is $976$

$k\frac{g}{m^3}.$

a$.$ Calculate the generalized Reynolds number and also the pressure drop using Eq$.(9\mathrm{.}1-9).$ Be

sure to convert $K$ to $K^{\text{'}}$ first.

b$.$ Repeat part $($a$)$ but use the friction factor method.

c$.$ Solve the power$-$law differential equation for this problem in MATLAB and plot shear stress

as function of $d\frac{v}{d}r.$