USE PYTHON, then Implement the given given codes for plotting

Problem $1(50=25+10+15)$

The resistance to flow in coeduits$/$pipes is parameterized by a dimensionless number called the friction

factor $(f).$ For turbulent flow, the Cole$$rook equation provides a means to calculate the friction factor:

$0-\frac{1}{\sqrt[\phantom{2}]{7}}+2\mathrm{.}0lo{g}_{10}(\frac{lon}{3\mathrm{.}7D}+\frac{2\mathrm{.}51}{Rc\sqrt[\phantom{2}]{7}})$

where $lon$ is roughaess in the pipe $($mam$),D$ is diameter of the pipe $($in m$),$ and $Re-\frac{\text{d}\text{e}\text{l}\text{V}\text{D}}{}$ is the Reynolds

number of the flow. $V$ is the velocity of the flow in the pipe $(\frac{m}{s}$ is the dynamic viscosity of the fluid

$(N,\frac{s}{m^2}),$ and $$ is density of the fluid $(k\frac{g}{m^3}).$

$($a$)$ Write a code to Calculate the friction factor $(f)$ for $-0\mathrm{.}003mm,$ for a range of Reynolds mum$-$

ber $(Re-{10}^4-{10}^6)$ and pipe Diameter $(D-{10}^{-1}-10(m))$ using the Colebrook equation Equ. $(1).$

Implenernt the equation$-$solving technique of your doice, e$.$g$.,$ Fixod$-$Point Iteration, Newton$-$Raphson,

Secant, or Modified$-$Secant. Note that friction factors $(f)$ uswally range between $0\mathrm{.}008$ to $0\mathrm{.}08.$

$($b$)$ Use "contourf" to plot the variation of $f$ with respect to $Re$ and $D$ calculated in part $($a$).$ In

addition, on the same figure also plot $f$ approsimated using the explicit formula called the Swanse$-$Jain

equation:

$f=\frac{1\mathrm{.}325}{[ln(\frac{t}{5\mathrm{.}7D}+\frac{5\mathrm{.}74}{\sqrt[\phantom{2}]{5t}}){]}^2}$

Hint: You many refer to the following codes for the plotting,

fig.aubplota$\_$ad juat $($bottor$=0\mathrm{.}1,$ top$-0\mathrm{.}9,$ left$-0\mathrm{.}1,$ right$-0\mathrm{.}8,$

waphese$-0\mathrm{.}4,$ hapace$-0\mathrm{.}1)$

: Plot friction factor va$.$ Reynolda mumber and pipe diaseter

plt$.$figure$($figaize$=(12,6))$

plt$.$ aubplot $(12$t$)$

plt$.$ contourf $($Re$\_$range, D$\_$range, friction$\_$factora, cmap$=$'viridia'$)$

plt$.$xlabel $(\text{'}$Reynolda Samber $($Re$)\text{'})$

plt$.$ylabel $(\text{'}$Pipe Diasater $(a{)}^{\text{'}})$

plt$.$tiele$(\text{'}$Priction Factor va$.$ Reyzolda Muzber and Pipe Diasater'$)$

ple.elia$(-0\mathrm{.}01,0\mathrm{.}035)$

ax $=$ Iig.add$\_$aubplot $(131)$

I Sviatee$-$Jain equation for compariabo

p$1$t$.$aubplot $(122)$

plt$.$colarbar $($label$=\text{'}$ Friction Factor $($I$)\text{'})$

ple.xlabel$(\text{'}$Beynolda Samber $($Re$)\text{'})$

plt$.$ylabel$(\text{'}$Pipe Diaseter $($a$)\text{'})$

plt$.$ticle$(\text{'}$Swasee$-$Jai$=$ Priction Pactor va$.$ Rajaolda Muzber and Pipe Diasater'$)$

ple.elia$(-0\mathrm{.}01,0\mathrm{.}035)$

$($c$)$ For a circular pipe the pressure required per uxit length of pipe is given by

$\frac{P}{L}=f(\frac{2}{{}^2{D}^3}{Q}^2)$

where $\frac{AF}{T}$ is the pressure gradient, defined as the pressure drop per leagth of pipe, $Q$ is the valume flow

rate $(m^3{s}^{-1})$ in the pipe, and $Q-V\frac{D^2}{4}.$ Calculate and plot pressure gradient as a function of $Q$

using equation $3$ when $D-2m,$ roughness $lon=0\mathrm{.}003mm,g=9\mathrm{.}81\frac{m}{s^2},$ density of water $=1000k\frac{g}{m^3},$

and dynamic viscosity of water $={10}^{-3}N*\frac{5}{m^2}.$ For calculatiag friction factor $f,$ you may use Equ.

$(1)$ or $(2).$ But, please justify your choice.