Question $4$

$($a$)$ Two large reservoirs are connected by two pipes. The difference in water

surface elevation of the reservoirs is $45m.$ The first pipe is $0\mathrm{.}3m$ diameter with

$=0\mathrm{.}06$ and the second pipe is $0\mathrm{.}5m$ diameter with $=0\mathrm{.}08.$ The two pipes

follow different routes between the two reservoirs such that the first pipe is $3\mathrm{.}9$

$km$ long and the second pipe is $4\mathrm{.}2km$ long. Determine the velocity of the flow

through each pipe and the total flow from the upper reservoir to the lower

reservoir. $[8$ marks$]$

$($b$)$ A cylindrical shaped water tower is to be drained for maintenance. It

measures $15m$ in diameter and holds water to a depth of $19m.$ The water

surface is at $148m$ O$.$D$.$ It will be drained via a single outlet pipe which draws

water from the bottom of the reservoir and discharges to the atmosphere just

above a stream. The pipe is $200m$ long, $0\mathrm{.}2m$ in diameter, has friction factor $$

$=0\mathrm{.}12$ and the outlet $($i$.$e$.$ the end of the pipe$)$ is at $123m$ O$.$D$.$ Calculate the

time it will take to empty the water tower. $[12$ marks$]$