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Refrigeration Formulas

Compression work, coefficient of performance and more

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Compression Work 

Compressor 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

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 

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)  

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