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For minimum work input in a two-stage compression process the intermediate pressure is the
- a)Arithmetic mean of suction and discharge pressure
- b)Logarithmic mean of suction and discharge pressure
- c)Geometric mean of suction and discharge pressure
- d)Hyperbolic mean of suction and discharge pressure
Correct answer is option 'C'. Can you explain this answer?
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For minimum work input in a two-stage compression process the intermed...
For minimum work input during compression precess,
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For minimum work input in a two-stage compression process the intermed...
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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