Question

1. In the UK, 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 $(0.03+(36/100))/kWh at night and is willing to pay $(0.08+(36/100))/kWh for power produced during the day. To take advantage of this opportunity, an entrepreneur is considering building a large reservoir (40+(36/10)) m above the lake level, pumping water from the lake to the reservoir at night using cheap power, and letting the water flow from the reservoir back to the lake during the day, producing power as the pump–motor operates as a turbine–generator during reverse flow. Preliminary analysis shows that a water flow rate of (2+(36/100)) m³/s can be used in either direction, and the irreversible head loss of the piping system is (4+(36/1000)) m. The combined pump–motor and turbine–generator efficiencies are expected to be 75 percent each. Assuming the system operates for 10 h each in the pump and turbine modes during a typical day, determine the potential revenue this system can generate per year.

The entrepreneur decided to play with the piping diameters in order to increase power generation. He chose a pipe area upstream of the pump-turbine system as (0.03+(36/1000)) m² and a diameter of (0.03+(36/1000)) m² downstream of the pump-turbine system. How would this affect his revenue.

Answer 1

Bomulls equation between lake and esclovir sy considering Pump and motor mode, resoviy hump = 2 24 +2, + V2 V sq 2g + 2+ h turbine : 1,20 V2=0 2,20 Piz Paton P2 = Patm h Pump = 7th turbine = 50+2 (e) = 52.om lake and cheselvior by considering turbine generator mode P + 1 + 2, thump = h + V2 + Z₂+ hnesine P, = P2 = Patin the V = V270 as Scanned WZ2-0 CamScanner Pump = 0

h turbine = zih hturbine - 50-2.8 htubine 47.2 » The work done by Pump = Sghe - Sghpump a - 1650 x2x9.01x52.0 Pump 10349340 done by Eletric Pouch using Pump → work Weletric = WPump 0.15 - 01361248 m → work done by turbine wasine = 25vghtwabine = 0.35 x 18 8 x 2 x 9.01 x 47.2 = 69454 & w Cost Peg night = 1381248 x0.06x10 1600 = $ 20. 7488 cost for a read = $828.7488 x 365 - $302493.312 Scanned with CamScanner