Problem$-1.$ Two reservoirs are connected by a $190m$ long, $100mm$ diameter ductile iron

pipe for which the roughness height is estimated to be $0\mathrm{.}3mm.$ The difference of water surface

elevations between the two reservoirs is $5m.$ The minor losses have been estimated to be $5\mathrm{.}4$

times the velocity head. The pump recommended to transfer water from the lower to the upper

reservoir has the characteristics curve described by:

$h_p=-400\mathrm{.}0245Q^2$

where

$hp$ is the head in meters and $Q$ is discharge in $\frac{L}{s}.$

$($a$)$ Determine the system demand equation.

$($b$)$ Plot the system demand and pump characteristics curve in a single diagram.

$($c$)$ Determine the discharge and head at the operating point. Assume the flow to be

in a fully turbulent regime.