$13\mathrm{.}5($Welty $13\mathrm{.}15,12$ pts $)$ Two water reservoirs of height $h_1=60m$ and $h_2=30m$ are connected by a

pipe that is $0\mathrm{.}35$ m in diameter. The exit of the pipe is submerged at distance $h_3=8m$ from the reservoir

surface.

a$.$ Determine the flow rate through the pipe if the pipe is $80$ m long and the friction factor $f_f=0\mathrm{.}004.$

The pipe inlet is set flush with the wall.

Hints:

i$)$ First do an energy balance between the two tanks. Assume pseudo$-$steady state, which means that tank

heights are constant for a snapshot in time. In other words, neglect the fact that the tank heights change

slowly over longer time periods. Note that the velocity in each tank is zero. Do not neglect head loss, $h_L.$

From $h_L$ calculate a starting guess for velocity in the pipe.

ii$)$ Do an energy balance on the pipe. Find the velocity in the pipe via iteration so that required energy

values are satisfied.

b$.$ If the relative roughness e$/$D $0\mathrm{.}004,$ determine the friction factor and flow rate