Find the steel pipe diameter required to convey a minimum of $\backslash (500\backslash$mathrm$\{$lit$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ of water. The pipe length is $18$ Km $,$ the difference in head between pipe ends is $\backslash (45\backslash$mathrm$\{$~m$\},\backslash$mathrm$\{$f$\}=0\mathrm{.}02\backslash )$ and the minor losses is $\backslash (15\backslash$mathrm$\{$v$\}2/2\backslash$mathrm$\{$~g$\}\backslash ).$ The pipe diameters available in the market are to the nearest $10$ cm $.$ What is the flow through the pipe you have chosen? If a valve is erected at the middle of the pipe length to adjust the flow to be exactly $\backslash (0\mathrm{.}4\backslash$mathrm$\{$~m$\}3/\backslash$mathrm$\{$sec$\}\backslash ),$ what would be the valve head loss? If the expected annual reduction in the flow is $\backslash (1\backslash \%\backslash ),$ give an estimation for the pipe absolute roughness after $4$ years of operation.

Figure $(2)$