b$)$ Two reservoirs are connected by two parallel pipelines with diameters of

$800$ mm and $600$ mm as shown in Figure $4\mathrm{.}1$ below. The pipelines are

both $2\mathrm{.}6$ km long with roughness factor $=0\mathrm{.}05.$ The combined discharge

through the pipelines must be at least $1\mathrm{.}7\frac{m^3}{sec}.$

I$)$ When the total discharge is $1\mathrm{.}7\frac{m^3}{sec},$ what is the flow rate in the

individual pipelines?

ii$)$ If the larger pipe has to be taken out of service for maintenance,

what proportion of the total discharge will be lost?

iii$)$ What is the minimum difference in the elevation of the surface

water level in the two reservoirs required to maintain a flow of $1\mathrm{.}7$

$\frac{m^3}{sec}$ through the pipeline?

$($Darcy$-$Weisbach: $h_f=\frac{L}{D}\frac{v^2}{2g})$