To calculate the compression efficiency and the overall efficiency, let’s break down the problem step by step:

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Given Data:

1. Compressor capacity: $800 \, \text{cfm}$
2. Suction pressure: $14.7 \, \text{psia}$
3. Discharge pressure: $110 \, \text{psia}$
4. Indicated work of compressor: $155 \, \text{hp}$
5. Indicated work of steam engine: $172 \, \text{hp}$

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(a) Compression Efficiency

The compression efficiency ($\eta_c$) is defined as:

$\eta_c = \frac{\text{Indicated Work of Compressor}}{\text{Indicated Work of Steam Engine}} \times 100\%$

Substitute the given values:

$\eta_c = \frac{155 \, \text{hp}}{172 \, \text{hp}} \times 100$

$\eta_c = 90.06\%$

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(b) Overall Efficiency

The overall efficiency ($\eta_o$) is defined as:

$\eta_o = \frac{\text{Indicated Work of Compressor}}{\text{Indicated Work of Steam Engine}} \times \text{Compression Efficiency} \times 100\%$

Substitute the values:

$\eta_o = \frac{155}{172} \times 0.9006 \times 100$

Perform the calculation:

$\eta_o = 81.16\%$

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Final Answers:

1. Compression Efficiency ($\eta_c$): $90.06\%$
2. Overall Efficiency ($\eta_o$): $81.16\%$

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Would you like to discuss further details or need assistance with related concepts?

Here are 5 follow-up questions to deepen your understanding:

1. How is indicated power measured in steam engines and compressors?
2. What factors can affect the compression efficiency of a compressor?
3. What is the difference between indicated power and brake power?
4. How does the suction and discharge pressure impact compressor efficiency?
5. How can the overall efficiency of a system like this be improved?

Tip: To ensure accurate calculations, always double-check unit conversions and verify the consistency of data provided.