Concept explainers
A pump-storage plant uses a turbine to generate hydropower during the day. letting water from the upper reservoir flow through the turbine Into the lower reservoir as sketched. The plant then pumps water back up to the upper reservoir during the night. In a typical pump-storage plant, the same turbomachine is used as both the pump and the turbine, and is called a punip-furbine. The plant is profitable because the demand for electric power is much higher during the day than it is at night, and utility companies sell power at much lower prices at night to encourage customers to use the available power generation capacity and to avoid building new expensive power plants that would 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 S0.030/kVh at night and is willing to pay $0.1 20/kWh for power produced during the day. A pump-storage plant has a gross head of 90.0 in, and can handle a volume flow rate of 4.6 m3/s in either direction. The irreversible head losses in the system are estimated as 5.0 m in either direction at this flow rate. The efficiency of the combined pump-motor is 88 percent and that of the combined turbine-generator is 92 percent. The plant runs in pump mode for 10 hours each night and runs in turbine mode for 10 hours each day. It operates 340 days in a year. How much net revenue (S) does this pump-storage plant generate in one year?
The plant net revenue generated in a year.
Answer to Problem 115P
The plant net revenue generated in a year is
Explanation of Solution
Given information:
The gross head of plant is, volume flow rate is
Write the expression for net head during electricity generation by turbine.
Here, gross head is
Write the expression for net head during electricity consumption by pump.
Write the expression for power generated by turbine.
Here, density of water is
Write the expression for power consume by pump.
Here, efficiency of pump-motor is
Write the expression for cost of electricity produced during day in a year.
Write the expression for cost of electricity consume during night in a year.
Write the expression for net revenue of the pump-turbine plant.
Calculation:
Substitute
Refer table "properties of saturated water" to obtain the density of water as
Substitute
Substitute
Substitute
Substitute
Substitute,
Substitute
Conclusion:
The plant net revenue generated in a year is
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Chapter 5 Solutions
Fluid Mechanics: Fundamentals and Applications