$14.$ Treated water at $\backslash (40^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is to be pumped into a deaerator as shown below, calculate the following:

a$)$ The system head loss. $(2\mathrm{.}45$ m $)$

b$)$ The pumping head required. $(59\mathrm{.}3$ m $)$

c$)$ The motor size required. $(23\mathrm{.}1$ kW $)$

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Data: $-$Flow rate $=100000$ kg$/$h$.$

$-$Pump efficiency $=70\%.$

$-$Suction and discharge piping and all fittings are $5$

inch sch$.40$ steel.

$-$Total pipe length $=50$ m$.$

$-$All elbows are $9\backslash$mp@subsup$\{0\}\{\}\{\backslash$circ$\},\backslash$textrm$\{$r$\}/\backslash$textrm$\{$d$\}=3.$

$-$Standard tees are used.

$-$All isolating valves are standard plug type gate

valves $(\}\backslash$beta$=1)\backslash$mathrm$\{.$

$-$Conventional swing check $($neglect effects of possible

over sizing$).$

$-$Entrance is inward projecting.

$-$Spray nozzles are spring loaded to maintain a pressure

drop of $70$ kPa.

$-$Level control valve is a butterfly type $($assume that

the valve is wide open$).$

$```$