The gravity system shown below should be designed to deliver a flow of $8000\frac{m^3}{h}$ with a pressure of $40mwc$ at the entrance of the city and a pipeline length of $1000m.$ Absolute roughness of the pipe can be assumed as $k_s=1mm$ and the water temperature equals $20C.$ Calculate:

a$)$ The piezometric head at the entrance of the city.

b$)$ The total head loss in the network $($assume minor losses are negligible$)$

c$)$ The hydraulic gradient, $S_f$

d$)$ The diameter of the pipeline to deliver the required flow. Adopt a degree of accuracy correct to one decimal place and begin iterations with a velocity of $2\mathrm{.}0\frac{m}{s}.$

e$)$ Is flow laminar, transitional, transitional turbulent or rough turbulent in the network?