For minimum work input in a two-stage compression process the intermediate pressure is thea)Arithmetic mean of suction and discharge pressureb)Logarithmic mean of suction and discharge pressurec)Geometric mean of suction and discharge pressured)Hyperbolic mean of suction and discharge pressureCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Explanation:

Two-Stage Compression Process:
In a two-stage compression process, the gas is compressed in two stages to achieve higher pressures. The work input required for compression primarily depends on the intermediate pressure between the suction and discharge pressures.

Minimum Work Input:
To minimize the work input in a two-stage compression process, the intermediate pressure should be the geometric mean of the suction and discharge pressures.

Geometric Mean:
The geometric mean is calculated by taking the square root of the product of two numbers. In the case of a two-stage compression process, the geometric mean of the suction pressure (P1) and the discharge pressure (P2) is given by the formula:
$$P_{intermediate} = \sqrt{P1 \times P2}$$

Reasoning:
The geometric mean is chosen for minimum work input because it provides a balanced approach between the suction and discharge pressures. This intermediate pressure helps in reducing the overall work input required for compression while maintaining efficient compression ratios.

Therefore, the geometric mean of the suction and discharge pressures is the optimal choice for achieving minimum work input in a two-stage compression process.

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