The water surface in a large reservoir $(A)$ is $40m$ above datum while the

surface elevation of a second reservoir $($C$)$ is at $10m$ above datum $($as

indicated in the sketch below$).$ A $750mm$ pipe with a length of $5,000m$ and a

Hazen$-$Williams $\text{'}C\text{'}$ of $130$ connects the reservoirs. There are two identical

pumps installed in a series operation in the pumping station. Each pump has

the following head$-$discharge curve

$H=20-9Q^{1\mathrm{.}8}$

in which $H$ is the total dynamic head of the pump $($in metres$)$ and $Q$ is the

pump discharge $($in cubic metres per second$).$

a$)$ Determine the flow in the pipeline system. Determine the maximum

ground elevation at location B $($located $1200m$ from the upstream

reservoir$)$ to provide a minimum pressure head of $25m$ at location $B.$

b$)$ If the ground elevation at location $B$ is $12m,$ what flow can the two pumps

in series provide while meeting a minimum pressure head of $25m$ at

location B$?$

c$)$ Would you recommend series or parallel operation of this system? Why?