Thermodynamics

Chapter 2 | 85Then the rate at which mechanical energy is supplied to the turbine by thefluid and the overall efficiency become0 ¢E # mech,fluid 0 m # 1e mech,in e mech,out 2 15000 kg>s210.491 kJ>kg2 2455 kWh overall h turbinegen W# elect,out0 ¢E # mech,fluid 0(b) Knowing the overall and generator efficiencies, the mechanical efficiencyof the turbine is determined fromh turbinegen h turbine h generator S h turbine h turbinegenh generator 0.760.95 0.80(c) The shaft power output is determined from the definition of mechanicalefficiency,W # shaft,out h turbine 0 ¢E # mech,fluid 0 10.80212455 kW2 1964 kW1862 kW2455 kW 0.76Discussion Note that the lake supplies 2455 kW of mechanical energy tothe turbine, which converts 1964 kW of it to shaft work that drives the generator,which generates 1862 kW of electric power. There are losses associatedwith each component.60 hpEXAMPLE 2–17Cost Savings Associated with High-EfficiencyMotorsA 60-hp electric motor (a motor that delivers 60 hp of shaft power at fullload) that has an efficiency of 89.0 percent is worn out and is to bereplaced by a 93.2 percent efficient high-efficiency motor (Fig. 2–61). Themotor operates 3500 hours a year at full load. Taking the unit cost of electricityto be $0.08/kWh, determine the amount of energy and money savedas a result of installing the high-efficiency motor instead of the standardmotor. Also, determine the simple payback period if the purchase prices ofthe standard and high-efficiency motors are $4520 and $5160, respectively.h = 89.0%60 hpStandard MotorSolution A worn-out standard motor is to be replaced by a high-efficiencyone. The amount of electrical energy and money saved as well as the simplepayback period are to be determined.Assumptions The load factor of the motor remains constant at 1 (full load)when operating.Analysis The electric power drawn by each motor and their difference canbe expressed ash = 93.2%High-Efficiency MotorFIGURE 2–61Schematic for Example 2–17.W # W # electric in,standard W # shaft>h st 1Rated power21Load factor2>h stelectric in,efficient W # shaft>h eff 1Rated power21Load factor2>h effPower savings W # electric in,standard W # electric in,efficient 1Rated power2 1Load factor211>h st 1>h eff 2