Total Work Done Per Cycle In Compressor During Incomplete Intercooling Given Volume Calculator

Formula Used:

\[ W = \frac{n_c}{n_c-1} \times P_1 \times V_1 \times \left(\left(\frac{P_2}{P_1}\right)^{\frac{n_c-1}{n_c}} - 1\right) + \frac{n_c}{n_c-1} \times P_2 \times V_2 \times \left(\left(\frac{P_3}{P_2}\right)^{\frac{n_c-1}{n_c}} - 1\right) \]

Polytropic Index for Compression (n_c):

Suction Pressure of Low Pressure Compressor (P₁):

Suction Volume (V₁):

m³

Discharge Pressure of Low Pressure Compressor (P₂):

Discharge Volume (V₂):

m³

Discharge Pressure of High Pressure Compressor (P₃):

Work Done Per Cycle (W):

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1. What is the Work Done Per Cycle Formula?

The formula calculates the total work done per cycle in a two-stage compressor with incomplete intercooling. It accounts for the polytropic compression process in both low-pressure and high-pressure stages of the compressor system.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( W \) — Work done per cycle (J)
\( n_c \) — Polytropic index for compression
\( P_1 \) — Suction pressure of low pressure compressor (Pa)
\( V_1 \) — Suction volume (m³)
\( P_2 \) — Discharge pressure of low pressure compressor (Pa)
\( V_2 \) — Discharge volume (m³)
\( P_3 \) — Discharge pressure of high pressure compressor (Pa)

Explanation: The formula calculates work for both compression stages, accounting for the polytropic process and pressure ratios at each stage.

3. Importance of Work Calculation

Details: Accurate work calculation is crucial for compressor efficiency analysis, energy consumption estimation, and proper system design in refrigeration and air conditioning applications.

4. Using the Calculator

Tips: Enter all pressure values in Pascals, volume values in cubic meters, and ensure the polytropic index is greater than 1. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is polytropic index for compression?
A: The polytropic index (n_c) characterizes the compression process where PVⁿ = constant. For air compression, it typically ranges from 1.2 to 1.4.

Q2: Why two-stage compression with intercooling?
A: Two-stage compression with intercooling reduces work input, lowers discharge temperature, and improves overall compressor efficiency compared to single-stage compression.

Q3: What is incomplete intercooling?
A: Incomplete intercooling occurs when the refrigerant is not cooled to the initial suction temperature between compression stages, resulting in higher intermediate pressure.

Q4: How does this differ from complete intercooling?
A: With complete intercooling, the refrigerant is cooled to the initial temperature, while incomplete intercooling results in higher temperature and different volume conditions.

Q5: What are typical applications of this calculation?
A: This calculation is used in refrigeration systems, air compressors, and industrial gas compression systems where two-stage compression with intercooling is employed.