formula's

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Compression Work Compression work can expressed as W = h q (1) where W = compression work (Btu min) h = heat of compression (Btu/lb) q = refrigerant circulated (lb/min) Compression Horsepower Compression horsepower can be expressed as P = W / 42.4 (2) where P = compression power (hp) W = compression work (Btu min) Alternatively P = c / (42.4 COP) (2b) where P = compression power (hp) c = capacity (Btu/min) COP = coefficient of performance Compression horsepower per Ton p = 4.715 / COP (2c) where p = compressor horsepower per Ton (hp/Ton)

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Page 1: Formula's

Compression Work 

Compression work can expressed as

W = h q  (1)

where 

W = compression work (Btu min)

h = heat of compression (Btu/lb)

q = refrigerant circulated (lb/min)

Compression Horsepower

Compression horsepower can be expressed as

P = W / 42.4   (2)

where 

P = compression power (hp)

W = compression work (Btu min)

Alternatively 

P = c / (42.4 COP)   (2b)

where 

P = compression power (hp)

c = capacity (Btu/min)

COP = coefficient of performance

Compression horsepower per Ton

p = 4.715 / COP  (2c)

where 

p = compressor horsepower per Ton (hp/Ton)

COP = coefficient of performance

COP - Coefficient of Performance

Page 2: Formula's

COP = NRE / h   (3)

where 

COP = Coefficient of Performance

NRE = Net Refrigeration Effect (Btu/lb)

h = heat of compression (Btu/lb)

Net Refrigeration Effect 

Net refrigeration effect can be expressed as

NRE = hl - he    (4)

where 

NRE = Net Refrigeration Effect (Btu/lb)

hl = enthalpy of vapor leaving evaporator (Btu/lb)

he = enthalpy of vapor entering evaporator (Btu/lb)

Capacity

c = q NRE    (5)

where 

c = capacity (Btu/min)

q = refrigerant circulated (lb/min) 

NRE = Net Refrigeration Effect (Btu/lb)

Compressor Displacement

d = c v / NRE   (6)

where 

d = compressor displacement (ft3/min)

c = capacity (Btu/min)

v = volume of gas entering compressor (ft3/lb)

NRE = Net Refrigeration Effect (Btu/lb)

Heat of Compression 

Page 3: Formula's

h = hlc - hec     (7)

where 

h = heat of compression (Btu/lb)

hlc = enthalpy of vapor leaving compressor (Btu/lb)

hec = enthalpy of vapor entering compressor (Btu/lb)

Volumetric Efficiency 

μ = 100 wa / wt     (8)

where 

μ = volumetric efficiency

wa = actual weight of refrigerant

wt = theoretical weight of refrigerant

Compression Ratio

CR = ph / ps   (9)

where 

CR = compression rate

 ph = head pressure absolute (psia) 

ps = suction pressure, absolute (psia)  

Page 4: Formula's

p-H Diagrams The pressure enthalpy (p-H) diagram is a useful way to show changes in system pressure and energy changes.  The refrigerant exists as a mixture of vapour and liquid under the Saturated Liquid and Saturated Vapour line.To the left of the Saturated Liquid line the refrigerant exists as a liquid.To the right of the Saturated Vapour line the refrigerant exists as a superheated vapour.On the diagram, the refrigeration cycle is represented by the line 1-2-3-4.1-2 is where the gas is compressed causing a rise in pressure and enthalpy which equalsthe energy put into the gas by the compressor, all in the superheat region.2-3 is where the gas is condensed to a liquid.3-4 is where the liquid / vapour is passed through an expansion device, the pressure is reduced without any enthalpy change.4-1 is where the liquid / vapour is evaporated completely to a gas and where enthalpy is extracted from surroundings. This is the REFRIGERATION or COOLING effect as shown below.  

Page 5: Formula's

Line 2-2’ represents cooling of the superheated gas in the condenser down to the saturated vapour temperature.The remainder of the condensing takes place from 2’-3 where latent heat is removed.If the condenser can sub-cool the refrigerant to a temperature less than saturation vapour temperature then extra Cooling Effect will result as shown below.The work input at the compressor can also be determined from the p-H diagram as shown below. 

Page 6: Formula's

                      A

typical p-H diagram can be shown for refrigerant R134a. 

Page 7: Formula's

Compressor Work It can be seen from the above diagram that the compressor compresses refrigerant from 3.5 bar to 10 bar.The suction pressure is therefore 3.5 bar.The delivery pressure is 10 bar.The Work Input to the compressor is 315 kJ/kg - 242 kJ/kg = 73 kJ/kg.The Compressor Work can be calculated as follows; 

W comp  =     m ref  (h2 - h1) Where;

W comp =           Compressor work (kW)            m ref      =          Mass flow rate of refrigerant (kg/s)            h2         =          Specific enthalpy at point 2 (kJ/kg)                   h1         =          Specific enthalpy at point 1 (kJ/kg)        If the refrigerant flow rate in the above example is 0.3 kg/s then the compressor work is;

 W comp  =     m ref  (h2 - h1)

Page 8: Formula's

W comp  =     0.3  (73)W comp  =     21.9 kW 

Refrigeration Effect The Refrigeration Effect can also be determined from the above diagram by using the following formula;                    RE    =       m ref  (h1 – h4)Where;

RE       =         Refrigeration or Cooling Effect (kW)            m ref      =          Mass flow rate of refrigerant (kg/s)            h1         =          Specific enthalpy at point 1 (kJ/kg)                   h4         =          Specific enthalpy at point 4 (kJ/kg)                           RE     =       0.3  (242 – 68)                   RE     =       0.3 ( 174)                   RE     =       52.2 kW.          Coefficient Or Performance The Coefficient of Performance is an indication of how efficient a refrigeration system is. 

COP  =       Refrigeration Effect  / Work Inputor

COP =       RE   /  W comp

  

In this example the COP is;           COP     =    52.2  /  21.9    =    2.38  Efficient Running For efficient  running the Evaporator temperature should be as high as possible. This is restricted by the dew-point temperature in an air conditioning application. The Condenser temperature should be as low as possible. Maximum cooling is generally required in the hottest summer weather when the condensing arrangements are least efficient and caution is thus necessary in selecting an appropriate temperature.

Page 9: Formula's

 

Further Examination of p-H Diagram A p-H diagram with some more detail is shown below.  

 The stages in the cycle are as follows:Stage 1 to 2: the superheated vapour is compressed.Stage 2 to 3: the hot superheated vapour enters the condenser where the first part of the process is desuperheating.Stage 3 to 4: the hot vapour is condensed back to a saturated liquid.Stage 4 to 5: the liquid is subcooled before it enters the expansion valve (this may occur in the condenser, a second heat exchanger or in the pipework connecting the condenser with the expansion valve).Stage 5 to 6: the high pressure liquid passes through an expansion device.Stage 6 to 7: low pressure liquid refrigerant in the evaporator absorbs heat from the air or water being cooled and evaporates to become dry saturated vapour.Stage 7 to 1: the refrigerant vapour absorbs more heat while in the evaporator and while in the pipework joining the evaporator to the compressor, to become a superheated vapour.

Page 10: Formula's