Refrigeration Formulas and Calculations

Refrigeration formulas are mathematical equations used to calculate thermodynamic properties and performance of refrigeration systems. These formulas and their applications are used in refrigeration and air conditioning systems, including residential and commercial refrigerators, freezers, and air conditioners. They are also used in industrial refrigeration systems, such as those used in food processing, pharmaceuticals, and chemical production.

It’s also important to note that these formulas are based on ideal condition and actual performance of the system can be different from the calculated values.

Compression Work

Compression work is a fundamental concept in the field of refrigeration and air conditioning. It refers to the work done by a compressor to compress the refrigerant, which is essential for the refrigeration process to take place. In this process, the compressor increases the pressure and temperature of the refrigerant, causing it to absorb heat from the surrounding air or liquid.

The amount of work done by a compressor can be calculated using the compression work formula, which is given by W = h * q. In this formula, W represents the compression work in Btu/min, h represents the heat of compression in Btu/lb, and q represents the refrigerant circulated in lb/min.

The compression work formula is a simple yet powerful tool that can be used to determine the efficiency of a refrigeration system. By knowing the compression work and the amount of refrigerant circulated, it is possible to calculate the coefficient of performance (COP) of the system, which is a measure of its energy efficiency.

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Compression Horsepower

Compression horsepower is a measure of the power required to compress the refrigerant in a refrigeration or air conditioning system. It can be calculated using two different formulas, both of which are based on the compression work done by the compressor.

The first formula for compression horsepower is:

P = W / 42.4

Where P is the compression power in horsepower (hp), and W is the compression work in Btu/min.

Compression Horsepower Calculator (method 1)

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hp

The second formula for compression horsepower is:

P = c / (42.4 * COP)

Where P is the compression power in horsepower (hp), c is the capacity in Btu/min, and COP is the coefficient of performance.

Compression Horsepower Calculator (method 2)

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hp

The third formula for compression horsepower per Ton is:

p = 4.715 / (COP)

Where p is the compressor horsepower per Ton (hp/Ton) and COP is the coefficient of performance.

hp/Ton

COP – Coefficient of Performance

The Coefficient of Performance (COP) is a measure of the efficiency of a refrigeration or air conditioning system. It is defined as the ratio of the amount of cooling provided by the system to the amount of energy required to operate the system.

The formula for COP is:

COP = NRE / h

Where COP is the coefficient of performance, NRE is the net refrigeration effect in Btu/lb, and h is the heat of compression in Btu/lb.

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Btu/lb

Net Refrigeration Effect

Net Refrigeration Effect (NRE) is a measure of the amount of heat that is absorbed by the refrigerant as it flows through a refrigeration or air conditioning system. It is the difference between the enthalpy of the vapor leaving the evaporator and the enthalpy of the vapor entering the evaporator.

The formula for NRE is:

NRE = hl – he

Where NRE is the net refrigeration effect in Btu/lb, hl is the enthalpy of the vapor leaving the evaporator in Btu/lb and he is the enthalpy of the vapor entering the evaporator in Btu/lb.

Btu/lb

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Btu/lb

Capacity

Capacity is a measure of the amount of cooling provided by a refrigeration or air conditioning system. It is the product of the refrigerant circulated and the net refrigeration effect.

The formula for capacity is:

c = q * NRE

Where c is the capacity in Btu/min, q is the refrigerant circulated in lb/min, and NRE is the net refrigeration effect in Btu/lb.

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Btu/min

Compressor Displacement

Compressor Displacement refers to the volume of the refrigerant that is compressed by the compressor per unit time. It is the product of the volume of the gas entering the compressor and the compressor’s capacity divided by the net refrigeration effect.

The formula for compressor displacement is:

d = c * v / NRE

Where d is the compressor displacement in ft3/min, c is the capacity in Btu/min, v is the volume of gas entering compressor in ft3/lb, and NRE is the net refrigeration effect in Btu/lb.

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ft3/lb

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ft3/min

Heat of Compression

Heat of compression is a measure of the amount of heat added to the refrigerant by the compressor as it compresses the refrigerant. It is the difference between the enthalpy of the vapor leaving the compressor and the enthalpy of the vapor entering the compressor.

The formula for heat of compression is:

h = (hlc) – (hec)

Where h is the heat of compression in Btu/lb, hlc is the enthalpy of the vapor leaving the compressor in Btu/lb and hec is the enthalpy of the vapor entering the compressor in Btu/lb.

Btu/lb

Btu/lb

Btu/lb

Volumetric Efficiency

Volumetric Efficiency is a measure of how effectively a compressor is able to compress the refrigerant. It is defined as the ratio of the actual weight of refrigerant compressed by the compressor to the theoretical weight that would be compressed if the compressor were operating at 100% efficiency.

The formula for volumetric efficiency is:

μ = (100 * (wa)) / (wt)

Where μ is the volumetric efficiency, wa is the actual weight of refrigerant compressed by the compressor and wt is the theoretical weight of refrigerant that could be compressed if the compressor were operating at 100% efficiency.

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%

Compression Ratio

Compression Ratio (CR) is the ratio of the head pressure to the suction pressure of a refrigeration or air conditioning system. It is a measure of how much the refrigerant is compressed by the compressor.

The formula for compression ratio is:

CR = (ph) / (ps)

Where CR is the compression ratio, ph is the head pressure absolute in psia (pounds per square inch absolute) and ps is the suction pressure absolute in psia.

Compression Ratio Calculator

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psia

What is the difference between theoretical and actual performance of a refrigeration system?
Theoretical performance of a refrigeration system is calculated using refrigeration formulas, which are based on ideal conditions. However, actual performance can differ from the calculated values due to various factors such as friction, heat transfer, and other losses. These differences can be attributed to the assumptions made in the formulas, which may not accurately represent real-world conditions. Therefore, it’s essential to consider these limitations when designing and optimizing refrigeration systems.
How do I calculate the coefficient of performance (COP) of a refrigeration system?

The COP of a refrigeration system can be calculated using the formula: COP = Qc / W, where Qc is the heat removed from the cold side and W is the work input to the compressor. This formula is based on the first law of thermodynamics and provides a measure of the system’s efficiency. A higher COP indicates a more efficient system.

What is the significance of compression ratio in refrigeration systems?

The compression ratio is a critical parameter in refrigeration systems, as it affects the system’s efficiency and performance. It is defined as the ratio of the discharge pressure to the suction pressure. A higher compression ratio can lead to increased energy consumption, reduced efficiency, and potential compressor damage. On the other hand, a lower compression ratio can result in reduced capacity and efficiency. Optimal compression ratio depends on the specific application and refrigerant used.

How do I calculate the net refrigeration effect of a refrigeration system?

The net refrigeration effect can be calculated using the formula: Net Refrigeration Effect = Qc – Qh, where Qc is the heat removed from the cold side and Qh is the heat rejected to the hot side. This formula takes into account the heat transfer between the system and its surroundings, providing a more accurate representation of the system’s cooling capacity.

What is the role of volumetric efficiency in refrigeration systems?

Volumetric efficiency is a measure of the compressor’s ability to compress refrigerant gas. It is defined as the ratio of the actual volume of gas compressed to the theoretical volume. A higher volumetric efficiency indicates a more efficient compressor, resulting in reduced energy consumption and increased system performance. Factors such as compressor design, suction and discharge valve performance, and refrigerant properties affect volumetric efficiency.

How do I calculate the heat of compression in a refrigeration system?

The heat of compression can be calculated using the formula: Heat of Compression = mc \* Cp \* (Td – Ts), where mc is the mass flow rate of the refrigerant, Cp is the specific heat capacity of the refrigerant, Td is the discharge temperature, and Ts is the suction temperature. This formula provides a measure of the energy required to compress the refrigerant, which affects the system’s overall efficiency and performance.

What are some common applications of refrigeration formulas in industry?

Refrigeration formulas have numerous applications in various industries, including food processing, pharmaceuticals, and chemical production. They are used to design and optimize refrigeration systems, ensuring efficient and reliable operation. For example, in cold storage facilities, refrigeration formulas are used to calculate the required cooling capacity, compressor sizing, and heat transfer rates. In industrial processes, these formulas are used to optimize refrigeration systems for specific applications, such as cryogenic cooling or temperature control.