3. From a test of an air compressor driven directly by a steam engine, the
following data and results were obtained: capacity, 800 cfm; suction at 14.7
psia; discharge at 110 psia; indicated work of the compressor, 155 hp; indicated
work of the steam engine, 172 hp. Calculate (a) the compression efficiency and
(b) the overall efficiency.
Answers: (a) 90.06%; (b) 81.16%

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

---

### **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**: \( 172 \, \text{hp} \)

---

### **(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:

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

\[
\eta_c = 90.06\%
\]

---

### **(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:

\[
\eta_o = 81.16\%
\]

---

### **Final Answers**:
1. **Compression Efficiency (\( \eta_c \))**: \( 90.06\% \)
2. **Overall Efficiency (\( \eta_o \))**: \( 81.16\% \)

---

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.

From a test of an air compressor driven directly by a steam engine, the following data and results were obtained: capacity, 800 cfm; suction at 14.7 psia; discharge at 110 psia; indicated work of the compressor, 155 hp; indicated work of the steam engine, 172 hp. Calculate (a) the compression efficiency and (b) the overall efficiency.

Learn how to calculate the compression efficiency and overall efficiency of an air compressor driven by a steam engine. Given data includes a capacity of 800 cfm, suction at 14.7 psia, discharge at 110 psia, and indicated works of 155 hp (compressor) and 172 hp (steam engine). Step-by-step solution with formulas provided. Suitable for Grades 10-12.

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