The Ergun equation, shown below, is used to describe the flow of a fluid through a packed bed. $P$ is the pressure drop, $$ is the density of the fluid, $G_0$ is the mass velocity $($mass flow rate divided by cross sectional area$),D_p$ is the diameter of the particles within the bed, $$ is the fluid viscosity, $L$ is the length of the bed, and $$ is the void fraction $($the fraction of the volume that is not solid; i$.$e$.$ consists of voids$)$ of the bed.

$\frac{P}{L}\frac{D_p}{G_o^2}\frac{{}^3}{(1-)}=\frac{150}{Re}(1-)+1\mathrm{.}75$

Given the parameter values listed below, find the void fraction $$ of the bed $($a$)$ graphically, $($b$)$ by using NewtonRaphson method to an approximation error of take your initial estimate as $+-10\%$ of your graphical estimate$).$

$G_o{D}_p=150$

$G_o^{2}L=0\mathrm{.}25(P)D_p$

$Re=G_o\frac{D_p}{}$