Answer Happy

The demand for electric power is usually much higher during the day than it is at night, and utility companies often sell power at night at much lower prices to encourage consumers to use the available power generation capacity and to avoid building new expensive power plants that will be used only a short time during peak periods. Utilities are also willing to purchase power produced during the day from private parties at a high price. Suppose a utility company is selling electric power for $0.04/kw hr at night and is willing to pay $0.135/kw hr for power produced during the day. To take advantage of this opportunity, an entrepreneur is considering building a large reservoir 200 m above the lake level, pumping water from the lake to the reservoir at night using cheap power and a pump, and letting the water flow from the reservoir back to the lake through a hydroelectric turbine during the day. Preliminary analysis shows that a water flow rate of 0.5 m³/s can be used in either direction, and the irreversible head loss of the piping system is 10 m in each direction. The combined pump- motor and turbine-generator efficiencies are expected to be 80 percent each. Also, assume that system operates for a duration 9 hours each night in "pump" mode and 9 hours each day in "turbine" mode. The density of water = 1000 kg/m³. 2b) Compute the minimum volume of the reservoir needed for the system; also, calculate the land usage requirements assuming an average reservoir depth of 5 m. 2c) Consider the addition of a wind turbine to provide electrical power, with an initial cost of $500,000 with a power output of 30,000 W. Calculate the potential increase in net income from this addition, and how long it will take to pay off the initial investment when ignoring the effects of interest. Assume the turbine runs 9 hours during the day selling power at 0.135 $/(kw hr) and runs 9 hours at night helping to power the pump. Ignore the remaining 6 hours of turbine operation. lower reservoir upper reservoir pump/turbine 200m