Centrifugal Compressor Power Calculator

Formula

The formula to calculate the Centrifugal Compressor Power (P) is:

\[ P = 2.31 \cdot \frac{k}{k-1} \cdot \left( \frac{To - Ti}{M} \right) \cdot Q \]

Where:

\( P \) is the power (kW)
\( k \) is the isentropic gas coefficient
\( To \) is the outlet temperature (°C or K)
\( Ti \) is the inlet temperature (°C or K)
\( M \) is the molar weight of the gas (g/mol)
\( Q \) is the throughput (t/h)

Definitions

Centrifugal Compressor Power (P): The power required to run a centrifugal compressor. It can also refer to the power produced by the compressor.
Isentropic Gas Coefficient (k): A coefficient that describes the isentropic process of the gas.
Outlet Temperature (To): The temperature of the gas at the outlet of the compressor.
Inlet Temperature (Ti): The temperature of the gas at the inlet of the compressor.
Molar Weight of the Gas (M): The molar weight of the gas being compressed.
Throughput (Q): The amount of gas passing through the compressor per unit time.

Example

Let's say the Isentropic Gas Coefficient (k) is 1.4, the Outlet Temperature (To) is 300 K, the Inlet Temperature (Ti) is 290 K, the Molar Weight of the Gas (M) is 28 g/mol, and the Throughput (Q) is 100 t/h. Using the formula:

\[ P = 2.31 \cdot \frac{1.4}{1.4 - 1} \cdot \left( \frac{300 - 290}{28} \right) \cdot 100 \]

We get:

\[ P \approx 288.75 \text{ kW} \]

So, the Centrifugal Compressor Power is approximately 288.75 kW.

Extended information about "Centrifugal-Compressor-Power-Calculator"

Centrifugal Compressor Power Formula

Definition: Calculate the power required for a centrifugal compressor.

Formula: \( P = \frac{\dot{m} \times R \times T_1}{\eta \times MW} \left( \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right) \)

\( P \): Power (in kW)
\( \dot{m} \): Mass flow rate (in kg/s)
\( R \): Universal gas constant (8.314 J/(mol·K))
\( T_1 \): Inlet temperature (in K)
\( \eta \): Efficiency
\( MW \): Molecular weight of the gas (in kg/mol)
\( P_2 \): Outlet pressure (in Pa)
\( P_1 \): Inlet pressure (in Pa)
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( P = \frac{2 \times 8.314 \times 300}{0.85 \times 0.028} \left( \left( \frac{200000}{100000} \right)^{\frac{1.4 - 1}{1.4}} - 1 \right) \)

\( \dot{m} \): 2
\( T_1 \): 300
\( \eta \): 0.85
\( MW \): 0.028
\( P_2 \): 200000
\( P_1 \): 100000
\( \gamma \): 1.4

Centrifugal Compressor Efficiency Calculation

Definition: Calculate the efficiency of a centrifugal compressor.

Formula: \( \eta = \frac{\text{Actual Work}}{\text{Ideal Work}} \)

\( \eta \): Efficiency
\( \text{Actual Work} \): Actual work done by the compressor
\( \text{Ideal Work} \): Ideal work required for compression

Example: \( \eta = \frac{150}{200} \)

\( \text{Actual Work} \): 150
\( \text{Ideal Work} \): 200

Compressor Power Calculation Formula

Definition: Calculate the power required for a compressor.

Formula: \( P = \frac{\dot{m} \times R \times T_1}{\eta \times MW} \left( \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right) \)

\( P \): Power (in kW)
\( \dot{m} \): Mass flow rate (in kg/s)
\( R \): Universal gas constant (8.314 J/(mol·K))
\( T_1 \): Inlet temperature (in K)
\( \eta \): Efficiency
\( MW \): Molecular weight of the gas (in kg/mol)
\( P_2 \): Outlet pressure (in Pa)
\( P_1 \): Inlet pressure (in Pa)
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( P = \frac{1.5 \times 8.314 \times 290}{0.9 \times 0.029} \left( \left( \frac{250000}{100000} \right)^{\frac{1.4 - 1}{1.4}} - 1 \right) \)

\( \dot{m} \): 1.5
\( T_1 \): 290
\( \eta \): 0.9
\( MW \): 0.029
\( P_2 \): 250000
\( P_1 \): 100000
\( \gamma \): 1.4

Compressor Power Consumption Formula

Definition: Calculate the power consumption of a compressor.

Formula: \( P = \frac{\dot{m} \times R \times T_1}{\eta \times MW} \left( \left( \frac{P_2}{P_1} \right)^{\frac{\gamma - 1}{\gamma}} - 1 \right) \)

\( P \): Power (in kW)
\( \dot{m} \): Mass flow rate (in kg/s)
\( R \): Universal gas constant (8.314 J/(mol·K))
\( T_1 \): Inlet temperature (in K)
\( \eta \): Efficiency
\( MW \): Molecular weight of the gas (in kg/mol)
\( P_2 \): Outlet pressure (in Pa)
\( P_1 \): Inlet pressure (in Pa)
\( \gamma \): Heat capacity ratio (Cp/Cv)

Example: \( P = \frac{2.5 \times 8.314 \times 310}{0.88 \times 0.030} \left( \left( \frac{300000}{100000} \right)^{\frac{1.4 - 1}{1.4}} - 1 \right) \)

\( \dot{m} \): 2.5
\( T_1 \): 310
\( \eta \): 0.88
\( MW \): 0.030
\( P_2 \): 300000
\( P_1 \): 100000
\( \gamma \): 1.4