Thermodynamics

102 | Thermodynamicsand the power generation potential of a wind turbine with 50-m-diameter blades at that location. Also determine the actualelectric power generation assuming an overall efficiency of30 percent. Take the air density to be 1.25 kg/m 3 .2–67 Reconsider Prob. 2–66. Using EES (or other)software, investigate the effect of wind velocityand the blade span diameter on wind power generation. Letthe velocity vary from 5 to 20 m/s in increments of 5 m/s,and the diameter vary from 20 to 80 m in increments of 20m. Tabulate the results, and discuss their significance.2–68 A wind turbine is rotating at 15 rpm under steadywinds flowing through the turbine at a rate of 42,000 kg/s.The tip velocity of the turbine blade is measured to be 250km/h. If 180 kW power is produced by the turbine, determine(a) the average velocity of the air and (b) the conversion efficiencyof the turbine. Take the density of air to be 1.31kg/m 3 .2–69 Water is pumped from a lake to a storage tank 20 mabove at a rate of 70 L/s while consuming 20.4 kW of electricpower. Disregarding any frictional losses in the pipes andany changes in kinetic energy, determine (a) the overall efficiencyof the pump–motor unit and (b) the pressure differencebetween the inlet and the exit of the pump.2–72 Large wind turbines with blade span diameters ofover 100 m are available for electric power generation. Considera wind turbine with a blade span diameter of 100 minstalled at a site subjected to steady winds at 8 m/s. Takingthe overall efficiency of the wind turbine to be 32 percent andthe air density to be 1.25 kg/m 3 , determine the electric powergenerated by this wind turbine. Also, assuming steady windsof 8 m/s during a 24-hour period, determine the amount ofelectric energy and the revenue generated per day for a unitprice of $0.06/kWh for electricity.2–73E A water pump delivers 3 hp of shaft power whenoperating. If the pressure differential between the outlet andthe inlet of the pump is measured to be 1.2 psi when the flowrate is 8 ft 3 /s and the changes in velocity and elevation arenegligible, determine the mechanical efficiency of this pump.2–74 Water is pumped from a lower reservoir to a higherreservoir by a pump that provides 20 kW of shaft power. Thefree surface of the upper reservoir is 45 m higher than that ofthe lower reservoir. If the flow rate of water is measured tobe 0.03 m 3 /s, determine mechanical power that is convertedto thermal energy during this process due to frictional effects.2Storage tank20 mPump0.03 m 3 /s45 m1z 1 = 0FIGURE P2–692–70 A geothermal pump is used to pump brine whose densityis 1050 kg/m 3 at a rate of 0.3 m 3 /s from a depth of 200m. For a pump efficiency of 74 percent, determine therequired power input to the pump. Disregard frictional lossesin the pipes, and assume the geothermal water at 200 m depthto be exposed to the atmosphere.2–71 Consider an electric motor with a shaft power output of20 kW and an efficiency of 88 percent. Determine the rate atwhich the motor dissipates heat to the room it is in when themotor operates at full load. In winter, this room is normallyheated by a 2-kW resistance heater. Determine if it is necessaryto turn the heater on when the motor runs at full load.20 kWPumpControl surfaceFIGURE P2–742–75 A 7-hp (shaft) pump is used to raise water to an elevationof 15 m. If the mechanical efficiency of the pump is 82percent, determine the maximum volume flow rate of water.2–76 A hydraulic turbine has 85 m of elevation differenceavailable at a flow rate of 0.25 m 3 /s, and its overall turbine–generator efficiency is 91 percent. Determine the electricpower output of this turbine.2–77 An oil pump is drawing 35 kW of electric powerwhile pumping oil with r 860 kg/m 3 at a rate of 0.1 m 3 /s.The inlet and outlet diameters of the pipe are 8 cm and 12 cm,