A centrifugal pump is delivering water from an underground tank to an overhead reservoir against a static head of $35$ m through a $2$ km long, $250$ mm diameter pipe. The head-discharge characteristic of the pump is given by
\[
H=140-9000 Q^{2}
\]
where $H$ is the head (in m ) generated by the pump and $Q$ is the discharge (in $\mathrm{m}^{3} / \mathrm{s}$ ) of the pump.
Neglecting all minor losses, the head (in m ) generated by the pump is $\_\_\_\_$ (rounded off to the nearest integer).
Use: $\text{Darcy-Weisbach friction factor} f=0.04$
$\text { Acceleration due to gravity }=9.81 \mathrm{~m} / \mathrm{s}^{2}$
$\pi=3.14$
