HYDRAULICS ASSIGNMENT #$2$

Question:

Three pipes A$,$ B and C are interconnected with each other as shown where the water is flowing within this system at $18\mathrm{.}5C.$ Over the figure topographic elevations $\text{'}z\text{'}$ of some points are also given. Along the pipe A$,$ there exists a single $($one$)$ water$-$pump $($its charateristics are detailed in the below appropriate table$).$ The pipe characteristics and the total minor loss coefficients for each pipe is given in the relevant table below. The working regions atmospheric pressure is $101\mathrm{.}300$kPa $($absolute$).$ Find the flow rate $\text{'}Q\text{'}$ passing in each pipe?

$\backslash$table$[[$Pipe$,$Diameter $\text{'}\text{'}($mm$),$Length $\text{'}L\text{'}($m$),{\displaystyle \underset{?}{\overset{?}{}}}{k}_{\text{m}\text{i}\text{n}\text{o}\text{r}}(-),$Material$],[$A$,150,4820,14\mathrm{.}6,$Rough riveted steel$],[$B$,120,680,23\mathrm{.}5,$PVC$],[$C$,250,1735,18\mathrm{.}9,$Galvanized iron$]]$

$\backslash$table$[[Q(1\frac{t}{s}),0,5,10,15,20,25,30,35,40,45],[Hp(m),9\mathrm{.}00,8\mathrm{.}90,8\mathrm{.}55,8\mathrm{.}00,7\mathrm{.}20,6\mathrm{.}20,4\mathrm{.}95,3\mathrm{.}50,1\mathrm{.}80,0],[(\%),0,34\mathrm{.}3,57\mathrm{.}8,73\mathrm{.}5,82\mathrm{.}6,75\mathrm{.}2,65\mathrm{.}3,49\mathrm{.}8,33\mathrm{.}9,0]]$

$[$The equation of the pump $\text{'}$Hp $-Q\text{'}$ characteristic is: $H_p=9\mathrm{.}0-0\mathrm{.}0045Q^2($where $Q$ is in It$/$s$)]$