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A steam plant has the boiler efficiency of 92%, turbine efficiency (mechanical) of 94%, generator efficiency of 95% and cycle efficiency of 44%. If 6% of the generated power is used to run the auxiliaries the overall plant efficiency is
  • a)
    34%
  • b)
    39%
  • c)
    45%
  • d)
    30%
Correct answer is option 'A'. Can you explain this answer?
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Overall Plant Efficiency Calculation:
The overall plant efficiency can be calculated by considering the efficiencies of each component in the steam plant. The given efficiencies are:

- Boiler efficiency: 92%
- Turbine efficiency (mechanical): 94%
- Generator efficiency: 95%
- Cycle efficiency: 44%

The efficiency of the overall plant is given by the product of the efficiencies of each component.

Overall Plant Efficiency = Boiler Efficiency * Turbine Efficiency * Generator Efficiency * Cycle Efficiency

Calculating Overall Plant Efficiency:
Plugging in the given values, we can calculate the overall plant efficiency.

Overall Plant Efficiency = 0.92 * 0.94 * 0.95 * 0.44
= 0.37

Thus, the overall plant efficiency is 37%.

Effect of Auxiliaries:
In addition to the main components of the steam plant, there are also auxiliaries that consume a portion of the generated power. It is mentioned that 6% of the generated power is used to run the auxiliaries.

To calculate the net power output of the plant, we need to subtract the power consumed by the auxiliaries from the total generated power.

Net Power Output = Total Generated Power - Power Consumed by Auxiliaries

Calculating Net Power Output:
Let's assume the total generated power is P.

Power Consumed by Auxiliaries = 0.06 * P

Net Power Output = P - 0.06 * P
= 0.94 * P

Calculating Plant Efficiency with Auxiliaries:
To calculate the overall plant efficiency considering the power consumed by auxiliaries, we need to divide the net power output by the total generated power.

Overall Plant Efficiency with Auxiliaries = Net Power Output / Total Generated Power
= (0.94 * P) / P
= 0.94

Therefore, the overall plant efficiency with the power consumed by auxiliaries taken into account is 94%.

Comparison:
Comparing the two plant efficiencies calculated, we can see that the overall plant efficiency without considering the power consumed by auxiliaries is 37%, while the overall plant efficiency considering the auxiliaries is 94%.

Since the question asks for the overall plant efficiency, the correct answer is option 'A', which states that the overall plant efficiency is 34%. However, this seems to be a mistake in the options provided, as the correct value is 37%.
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