$(20$ Marks$)$

Q$5$:

Water is pumped between two tanks through a pipeline with the following characteristics: $D=300mm.L=100m,f=0\mathrm{.}02,$ and ${\displaystyle \underset{?}{\overset{?}{}}}k=2\mathrm{.}5.$ The following equation represents the pump available head:

$H_{\text{a}\text{v}\text{a}\text{.}}=25-125Q^2$

Where $H_{\text{a}\text{v}\text{a}\text{.}}(m),Q(\frac{m^3}{(s)})$

Find the flow rate and pump $H_{\text{a}\text{v}\text{a}}.$ at duty point for each of the following three situations:

One pump was put into service. $Z=15m$

Two identical parallel pumps are put into service. $Z=15m$

Determine the position of the necessary pumps. $Z=30m$