The plumbing in your house is $3 / 4$ in. sch 40 galvanized pipe, and it is connected to an 8 in. sch 80 water main in which the pressure is $15 \mathrm{psig}$. When you turn on a facet in your bathroom (which is $12 \mathrm{ft}$ higher than the water main), the water flows out at a rate of $20 \mathrm{gpm}$.

(a) How much energy is lost due to friction in the plumbing?

(b) If the water temperature in the water main is $60^{\circ} \mathrm{F}$, and the pipes are well insulated, what would the temperature of the water be leaving the faucet?

(c) If there were no friction loss in the plumbing, what would the flow rate be (in gpm)?