Pelton Wheel Un-Discussion Question

Your friend, Todd, has a cabin up by Mt. Shasta. His water system consists of a 15,000- gallon tank located 100 ft in elevation above the cabin. A 500-ft 2.5-inch diameter pipe connects the cabin and the tank. The tank is fed by a spring with enough flow to fill it in 12 hours (i.e. overnight). Because of water quality problems, Todd recently abandoned this system for drinking water and dug a well. Now he’s wondering if he can generate electricity by using a Pelton wheel. Todd has an old set of gears and a generator so that he can produce 60 cycle power if the Pelton wheel turns at 480 rpm. So, he’ll always want to maintain this speed. At your suggestion, he took several measurements of the pressure and flow at the end of the pipe. These are shown in the table below.

Your tasks are to determine: (1) the highest turbine power (in hp) and how long it can be sustained, and (2) the power that can be sustained for at least 5 hours per day. For both questions, specify the turbine diameter. Turbines are available in 2-inch increments from 8 inches to 16 inches. Assume that the efficiency curve you measured in the lab applies to all of these turbines (not in fact true). Assume that the water available per day is 15,000 gallons (i.e., when the tank is empty, it takes until the next day to refill).

Provide complete hand calculations for the first flow. You can program the other flows into a spreadsheet. Provide a printout in your submittal.

Extra credit (5 points): Assuming the electrical generator and gear set is 85% efficient, calculate the electrical power (in KW) that can be sustained for at least 5 hours per day and indicate whether it is enough to power a refrigerator and a clothes washer running simultaneously.

Field data Flow (gpm) Pressure at the end of the pipe (psi) 180 7 140 21 120 32 80 39 40 41