Problem $3(33$ points$)$

Austin Water wants to convey $5,000[m^3]$ of water per day from a reservoir to a water

treatment plant $10[km]$ away. The water surface of the reservoir is $5[m]$ above the entrance

of the pipe, and the water surface in the receiving tank is $1[m]$ above the exit of the pipe.

The pipe will be laid on a $\frac{1}{500}$ slope and will be made of concrete $($good joints$).$ A rotary

valve $(K_v=10)$ will be placed at the midpoint of the pipe to control flow from the reservoir.

Assume square$-$wall entrances at reservoirs. The temperature in the area averages $20C.$

List all minor losses and write out the head loss equation for each minor loss. Specify

the values of the loss coefficients. $(6$ points$)$

Draw the hydraulic grade line and energy grade line from the reservoir to the receiving

tank on the figure shown above. $(4$ points$)$

Write the energy equation from the reservoir to the receiving tank. Include full expres$-$

sions for all major and minor loss terms. Simplify as much as possible, and rearrange

such that the left hand side is equal to zero. Do not substitute numeric values into the

equation yet. $(8$ points$)$

What is the head loss $h_L=z_a-z_b$ between the reservoir and water treatment plant

in $m?(3$ points