# Calculating Cooling Loads

## Calculating chiller and cooling tower refrigeration - in tons

Cooling towers tons pairs the water-cooled chiller tons and the water-cooled condenser tons.

### Chiller Refrigeration Tons

The process of cooling is called refrigeration. For commercial and industrial refrigeration systems most of the world uses the kilowatt (kW) as the basic unit of refrigeration. Some commercial and industrial refrigeration systems are rated in Tons of Refrigeration (TR, tons).

A water-chiller refrigeration* ton* is defined as:

*1 Refrigeration Ton (RT) = 1 TONS_{cond} = 12000 Btu/h = 200 Btu/min = 3025.9 k Calories/h = 12661 kJ/h = 3.517 kW*

*1 kW = 0.2843 Refrigeration Ton (RT)*

A ton is the amount of heat removed by an air conditioning system that would melt *1 ton* *(2000 lbs.)* of ice in *24 hours. The heat required to melt 1 lb of ice at 32 ^{o}F to water is 144 Btu. *

*1 Ton Refrigeration = (2000 lb) (144 Btu/lb) / (24 hr) *

* = 12000 Btu/hr*

#### Converting between Btu/h and Tons of Refrigeration

Btu/h | Refrigeration Ton | kW |
---|---|---|

6000 | 1/2 | 1.76 |

12000 | 1 | 3.52 |

18000 | 1 1/2 | 5.28 |

24000 | 2 | 7.03 |

30000 | 2 1/2 | 8.79 |

36000 | 3 | 10.6 |

42000 | 3 1/2 | 12.3 |

48000 | 4 | 14.1 |

54000 | 4 1/2 | 15.8 |

60000 | 5 | 17.6 |

### Cooling Tower Tons

A cooling tower ton is defined as:

*1 cooling tower ton = 1 TONS _{evap} = 1 TONS_{cond} x 1.25 = 15000 Btu/h = 3782 k Calories/h = 15826 kJ/h = 4.396 kW*

The equivalent ton on the cooling tower side actually rejects about *15000 Btu/h* due to the heat-equivalent of the energy needed to drive the chiller's compressor. This equivalent ton is defined as the heat rejection in cooling *3 U.S. gallons/minute (1500 pound/hour)* of water *10°F*, which amounts to *15000 Btu/hour*, or a chiller coefficient-of-performance (COP) of *4.0* - a COP equivalent to an energy efficiency ratio (EER) of *13.65*.

### Heat Load and Water Flow

A water systems heat load in *Btu/h* can be simplified to:

h = c_{p}ρ q dt

=(1 Btu/lb_{m}^{o}F) (8.33 lb_{m}/US gal) q(60 min/h) dt

= 500 q dt(1)

where

h= heat load (Btu/h)

c_{p}= specific heat, 1 (Btu/lb_{m}^{o}F) for water

ρ = 8.33 (lb_{m}/US gal) for water

q= water volume flow rate (US gal/min)

dt= temperature difference (^{o}F)

### Example - Water Chiller Cooling

Water flows with *1 gal/min* and *10 ^{o}F* temperature difference. The ton of cooling load can be calculated as:

h = 500 (1 US gal/min) (10^{ o}F)

= 5000 Btu/h

= (5000 Btu/h) / (12000 Btu/ton)

= 0.42 ton