An off-grid, pumped hydro system, powered using a photovoltaic array, is designed to provide 10 kWh/day for a small cabin located near a pond, with a peak demand of 3 kW. A storage tank is placed on a nearby hilltop 100 feet above the turbine/generator. Pipe connections, each 800 feet in length, run to and from the tank.
a. Assuming an average head loss of 15% in the pipeline, and 80% conversion efficiency for the turbine/generator, how many gallons of water need to flow from the upper tank to the pond to supply the daily energy requirement for the cabin?
b. If the piping head losses are 20% during peak demand, what flow rate of water (in gpm, or gallons per minute) form the tank is needed to supply the 3 kW peak?
c. What size PVC pipe (in) will keep the friction head losses to 20% at peak demand? (Use the data provided in Figure 8.35 of Masters 2nd Edition, pictured below)
d. What surface area (m2) is needed for the photovoltaic collector to supply the daily energy requirement for the cabin, if the area receives 5.5 kWh/(m2day) of insolation?
Assume 15% head losses in each section of the pipeline to and from the storage tank, and a pump efficiency of 75%. Also, assume a 19% PV conversion efficiency of the insolation into electricity to power the pump.