Determine the friction factor, $f$ using the bisection method and the Newton$-$Raphson method.

For turbulent flow, the Colebrook equation can be used to approximate the friction factor.

$0=\frac{1}{\sqrt[\phantom{2}]{f}}+2\mathrm{.}0log(\frac{}{3\mathrm{.}7D}+\frac{2\mathrm{.}51}{Re\sqrt[\phantom{2}]{f}})$

where $=$ the roughness $(m),D=$diameter$(m)$ and $Re=$ the Reynolds number

$Re=\frac{VD}{}$

where $=$ the fluid' density $(k\frac{g}{m^3}),V=$ the velocity of fluid $(\frac{m}{s}),$ and $=$ dynamic viscosity $\frac{s}{m^2}.$

Use $=1\mathrm{.}23k\frac{g}{m^3},V=40\frac{m}{s},=1\mathrm{.}79{10}^{-5}N\frac{s}{m^2},D=0\mathrm{.}005m,=0\mathrm{.}0015.$

For the bisection method, $(1)$ use the friction factor range from $0\mathrm{.}008$ and $0\mathrm{.}08,$ and for the Newton$-$Raphson method, $(2)$ use the lower limit as an initial guess and $(3)$ use the upper limit as an initial guess.

Discuss each case in terms of number of iterations, percentage relative error, and the determined value. If the Newton$-$Raphson method does not converge, inspect why it does not converge.

Submit a zip file that includes a main python file, function file$($s$)($you can create one function file that has the bisection and Newton Raphson or two function files for each method$),$ and a pdf file for the discussion.