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MoistAirTab™ Example 8 - Multiple Stage Compression

Example 8

Air at 80°F, 740 mm Hg pressure and 55% relative humidity is compressed to 10 atm (gauge) in a 3-stage air compressor. The isentropic efficiency of the air compressor for each stage is 85%. Cooler/condensers are used to reduce the stage discharge temperature to 80°F. The pressure drop for each cooler is 3 psi. The compressed air flowrate is 25,000 lb/hr.

  1. What is the discharge temperature of the compressor (before any cooling)?
  2. What is the total brake horsepower required?

Solution

The solution is presented below as a table generated from Excel. The gray shaded areas represent the input data.

Solution: Inlet1st Stage2nd Stage3rd StageOverall
  1234567 
 UnitsAmbient Air1st Stage Compressor Outlet1st Stage Condenser Outlet2nd Stage Compressor Outlet2nd Stage Condenser Outlet3rd Stage Compressor Outlet3rd Stage Condenser OutletSummary
Flow ratelb/hr25,00025,00025,00025,00025,00025,00025,00025,000
Compression ratio  2.24 2.24 2.24 11.30
Number of stages        3
Pressuremm Hg740       
 atm0.972.181.984.904.7011.0010.80 
 psia14.3132.1129.1172.0569.05161.67158.67 
          
Pressure droppsia  3.00 3.00 3.00 
Temperature°F80.00240.0980.00247.8080.00284.0880.00 
Relative humidity%55%2.5%100%4.3%100%2.2%100% 
Humidity ratiolbw/lbdry air0.01240.01240.01110.01110.00470.00470.0021 
Moisture condensedlbw/hr  32.76 160.98 65.31 
          
Isentropic efficiency  87% 87% 87%  
Entropy of moist airBtu/(lbdry air.°F)0.05170.0591-0.00080.0024-0.0743-0.0551-0.1379 
Enthalpy of moist airBtu/lbdry air25.1564.5723.6164.8016.2865.8912.82 
          
Entropy (Ideal)Btu/lbdry air 0.0517 -0.0008 -0.0743  
Enthalpy (Ideal)Btu/lbdry air 59.44 59.44 59.44  
Enthalpy Difference (Ideal)Btu/lbdry air 34.29 35.83 43.16  
Enthalpy Difference (Real)Btu/lbdry air 39.41 41.19 49.61  
          
Specific volume of moist airft3/lbdry air14.258.246.993.712.911.721.26 
Volumetric flow rateACFM5,936.193,432.582,911.201,544.191,213.91717.38525.23 
          
Power InputBtu/hr 985,361  1,029,698  1,240,239   
Brake HorsepowerHP 391.79  409.42  493.14  1,294.35
Condenser DutyBtu/hr  (1,023,934) (1,212,869) (1,326,794) 
Temp rise in cooling wateroF  15 15 15 
Cooling water consumptionGPM  1,138  1,348  1,474 3,960