Need help with questions a$,$c$,$d and f only please.Thank you. Q$1.($a$)$ Darcy's equation, including additional friction due to fittings, can be written as:

$h_f=4(\frac{f}{2})\frac{u^2}{g}(\frac{L}{d}+\frac{L_e}{d})$

where $h_f$ is the friction head, $f$ is the Fanning friction factor and other symbols have their usual meaning. Explain how we use $\frac{L_e}{d}$ to account for friction losses in fittings, and how an 'equivalent length' of pipe to a fitting could be calculated.

$($b$)$ A cast iron pipeline has been proposed for conveying light oil of density $860kg{m}^{-3}$ and kinematic viscosity $5\mathrm{.}02{10}^{-6}{m}^2{s}^{-1}$ from a tanker to a storage tank. The pipeline will be $152\mathrm{.}5m$ long and the desired discharge rate is $101600kgh{r}^{-1}.$ The difference in height between the tanks is $24\mathrm{.}4m.$ A pump is available that is capable of developing a pressure of $3\mathrm{.}45{10}^{5}N{m}^{-2}.$ What is the calculated diameter of pipe required? Use a Fanning friction factor of $0\mathrm{.}007,$ ignore pressure loss due to pipe fittings, and provide a fully labelled diagram.

$d=0\mathrm{.}118$

$($c$)$ Assuming that pipe of the calculated diameter in Part $($b$)$ is not readily available, would you specify a pipe of smaller, or larger, diameter? Provide the reasoning for your choice.

$($d$)$ If the flow rate using your specified pipe diameter is larger than the desired rate $(101600$ kg hr ${?}^{-1}),$ how could you ensure that the desired flow rate is achieved? Use Darcy's equation to help explain your answer.

$($e$)$ Calculate the Reynolds Number of the flow using your calculated diameter from Part $($b$)$ and use this value to comment on the assumption of a constant value of friction factor. $,Re=71000$

$($f$)$ Check any other assumptions you have made in your answers to Parts $($b$)$ to $($d$)$ and comment on which side of a pump you would position any flow control equipment.