Thermodynamics

394 | ThermodynamicsThen the mass flow rate of air through a leak of minimum cross-sectionalarea A becomesm # 1>1k122air C discharge ak 1 b P line2A kR aRT line B k 1 b T line(7–90)where k is the specific heat ratio (k 1.4 for air) and C discharge is a discharge(or loss) coefficient that accounts for imperfections in flow at the leak site.Its value ranges from about 0.60 for an orifice with sharp edges to 0.97 for awell-rounded circular hole. The air-leak sites are imperfect in shape, andthus the discharge coefficient can be taken to be 0.65 in the absence of actualdata. Also, T line and P line are the temperature and pressure in the compressedairline, respectively.Once m . air and w comp,in are available, the power wasted by the leaking compressedair (or the power saved by repairing the leak) is determined fromPower saved Power wasted m # air w comp,in(7–91)EXAMPLE 7–22Energy and Cost Savings by Fixing Air LeaksThe compressors of a production facility maintain the compressed-air lines ata (gauge) pressure of 700 kPa at sea level where the atmospheric pressure is101 kPa (Fig. 7–75). The average temperature of air is 20°C at thecompressor inlet and 24°C in the compressed-air lines. The facility operates4200 hours a year, and the average price of electricity is $0.078/kWh. Takingthe compressor efficiency to be 0.8, the motor efficiency to be 0.92, and thedischarge coefficient to be 0.65, determine the energy and money saved peryear by sealing a leak equivalent to a 3-mm-diameter hole on the compressedairline.Solution An air leak in the compressed air lines of a facility is considered.The energy and money saved per year by sealing the leak are to bedetermined.Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas. 3Pressure losses in the compressed air lines are negligible.Analysis We note that the absolute pressure is the sum of the gauge andatmospheric pressures.Air inlet101 kPa20°CAir leakD ≈ 3 mmFIGURE 7–75Schematic for Example 7–22.MotorAirCompressor700 kPa24°C