Centrifugal Compressor Power Calculator, Formula, Centrifugal Compressor Power Calculation

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 (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:

1. 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.

2. 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: