__Centrifugal Compressor Power Calculator:__

__Centrifugal Compressor Power Calculator:__

Enter the values of specific heat ratio, k, outlet of the compressor, T_{o(K)}, inlet of the compressor, T_{i(K)}, molar weigth of the gas, M_{(g/mol)} and mass flow rate, Q_{(kg/s)} to determine the value of Centrifugal compressor power, P_{(kW)}.

__Centrifugal Compressor Power Formula:__

__Centrifugal Compressor Power Formula:__

Centrifugal compressor power (P) is the electrical power (watts) needed to run the compressor and increase gas pressure.

Specific heat ratio of the gas being compressed (air, for example, has a k of around 1.4) reflects how readily it absorbs heat during compression.

The difference between the outlet temperature (To) of the compressed gas and the inlet temperature (Ti) of the incoming gas. A larger temperature difference signifies more work done by the compressor, requiring more power.

The amount of gas mass (in kilograms per second, kg/s) the compressor processes. A higher mass flow rate translates to more gas being compressed per unit time, demanding more power.

Here, 2.31 is a constant, M is another constant often assumed to be 1 kg/K for air (representing the gas’s ability to store thermal energy).

Centrifugal compressor power, P_{(kW)} in kilowatts is calculated by multiplying a constant (2.31), the specific heat ratio, k of the gas being compressed (a dimensionless value), divided by (k – 1), by the temperature difference (T_{o(K)} – T_{i(K)}) between the outlet and inlet of the compressor in Kelvin divided by molar weigth of the gas, M_{(g/mol)} in grams per mole and then multiplying by the mass flow rate, Q_{(kg/s)} of the gas in kilograms per second.

Centrifugal compressor power, P_{(kW)} = 2.31 * k / (k – 1) * ((T_{o(K)} – T_{i(K)}) / M_{(g/mol)}) * Q_{(kg/s)}

P_{(kW)} = centrifugal compressor power in kilowatts, kW.

k = specific heat ratio.

T_{o(K)} = outlet of the compressor in Kelvin, K.

T_{i(K)} = inlet of the compressor in Kelvin, K.

M_{(g/mol)} = molar weight of the gas in grams per mole, g/mol.

Q_{(kg/s)} = mass flow rate in kilograms per second, kg/s.

__Centrifugal Compressor Power Calculation:__

__Centrifugal Compressor Power Calculation:__

- A centrifugal compressor is used for air (k = 1.4) with a mass flow rate of 2 kg/s. The inlet temperature is 300 K and the outlet temperature is 350 K. What is the power consumption of the compressor?

Given: k = 1.4, Q_{(kg/s)} = 2 kg/s, T_{o(K)} = 350 K, T_{i(K)} = 300 K

Centrifugal compressor power, P_{(kW)} = 2.31 * k / (k – 1) * ((T_{o(K)} – T_{i(K)}) / M_{(g/mol)}) * Q_{(kg/s)}

P_{(kW)} = 2.31 * 1.4 / (1.4 – 1) * ((350 K – 300 K) / M_{(g/mol)}) * 2 kg/s

(Note: We can assume M_{(g/mol) }= 1 kg/K for air for this calculation)

P_{(kW)} = 33.3 kW.

- A centrifugal compressor has a power consumption of 10 kW and operates on air (k = 1.4) with a temperature difference of 40 K (To – Ti = 40 K). The outlet temperature is 400 K (To). What is the mass flow rate of the air entering the compressor?

Given: P_{(kW)} = 10 kW = 10,000 W, k = 1.4, T_{o(K)} – T_{i(K) }= 40 K.

Centrifugal compressor power, P_{(kW)} = 2.31 * k / (k – 1) * ((T_{o(K)} – T_{i(K)}) / M_{(g/mol)}) * Q_{(kg/s)}

Q_{(kg/s) }= P_{(kW)} * M_{(g/mol) }/ (2.31 * k / (k – 1) * (To – Ti))

Assuming M = 1 kg/K for air:

Q_{(kg/s)} = 10000 * 1 / (2.31 * 1.4 / (1.4 – 1) * 40)

Q_{(kg/s) } = 0.73kg/s.

__Centrifugal Compressor Power:__

__Centrifugal Compressor Power:__