Thermodynamics

The water flow rate through the pump is 50 L/s. The diametersof the inlet and outlet pipes are the same, and the elevationdifference across the pump is negligible. If the pressuresat the inlet and outlet of the pump are measured to be 100kPa and 300 kPa (absolute), respectively, determine themechanical efficiency of the pump. Answer: 74.1 percent2–123 In a hydroelectric power plant, 100 m 3 /s of water flowsfrom an elevation of 120 m to a turbine, where electric power isgenerated. The overall efficiency of the turbine–generator is 80percent. Disregarding frictional losses in piping, estimate theelectric power output of this plant. Answer: 94.2 MWChapter 2 | 107efficiencies are expected to be 75 percent each. Disregardingthe frictional losses in piping and assuming the system operatesfor 10 h each in the pump and turbine modes during atypical day, determine the potential revenue this pump–turbinesystem can generate per year.Reservoir140 m100 m 3 /s120 mPump–turbine2LakeGenerator Turbineh turbine–gen = 80%FIGURE P2–1232–124 The demand for electric power is usually muchhigher during the day than it is at night, and utility companiesoften sell power at night at much lower prices to encourageconsumers to use the available power generation capacity andto avoid building new expensive power plants that will beused only a short time during peak periods. Utilities are alsowilling to purchase power produced during the day from privateparties at a high price.Suppose a utility company is selling electric power for$0.03/kWh at night and is willing to pay $0.08/kWh forpower produced during the day. To take advantage of thisopportunity, an entrepreneur is considering building a largereservoir 40 m above the lake level, pumping water from thelake to the reservoir at night using cheap power, and lettingthe water flow from the reservoir back to the lake during theday, producing power as the pump–motor operates as a turbine–generatorduring reverse flow. Preliminary analysisshows that a water flow rate of 2 m 3 /s can be used in eitherdirection. The combined pump–motor and turbine–generatorFIGURE P2–1242–125 A diesel engine with an engine volume of 4.0 L andan engine speed of 2500 rpm operates on an air–fuel ratio of18 kg air/kg fuel. The engine uses light diesel fuel that contains750 ppm (parts per million) of sulfur by mass. All ofthis sulfur is exhausted to the environment where the sulfur isconverted to sulfurous acid (H 2 SO 3 ). If the rate of the airentering the engine is 336 kg/h, determine the mass flow rateof sulfur in the exhaust. Also, determine the mass flow rate ofsulfurous acid added to the environment if for each kmol ofsulfur in the exhaust, one kmol sulfurous acid will be addedto the environment. The molar mass of the sulfur is 32kg/kmol.2–126 Leaded gasoline contains lead that ends up in theengine exhaust. Lead is a very toxic engine emission. The useof leaded gasoline in the United States has been unlawful formost vehicles since the 1980s. However, leaded gasoline isstill used in some parts of the world. Consider a city with10,000 cars using leaded gasoline. The gasoline contains 0.15g/L of lead and 35 percent of lead is exhausted to the environment.Assuming that an average car travels 15,000 km peryear with a gasoline consumption of 10 L/100 km, determinethe amount of lead put into the atmosphere per year in thatcity. Answer: 788 kg