---
title: "Cylinder output with clearance numerical"
subject: "Applied Thermodynamics"
chapter: 2
key: "semester_3/applied_thermodynamics:compressor-volumetric-efficiency-numerical"
source: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/compressor-volumetric-efficiency-numerical
site: BCT Engineering
---

# Cylinder output with clearance numerical

Applied Thermodynamics · Chapter 2: Air Compressors

- Asked in: year not given, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/applied_thermodynamics/compressor-volumetric-efficiency-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_3/applied_thermodynamics/chapter-2

## Question

A single-acting, single-cylinder air compressor has bore 150 mm, stroke 200 mm and runs at 300 rpm. The clearance volume is 5% of the swept volume. Air is drawn at 1 bar and 27 °C and delivered at 8 bar; compression and re-expansion follow $pV^{1.3} = C$. Find (a) the volumetric efficiency, (b) the volume of air drawn per minute at suction conditions, and (c) the indicated power.

## Short answer

With clearance ratio 5 % and pV^1.3 re‑expansion, volumetric efficiency = 80.3 %. Effective suction volume per cycle gives air drawn 0.851 m³/min; indicated power using that volume is 3.78 kW.

## Answer

#### Swept volume
$$
V_s = \frac{\pi}{4}d^2L = \frac{\pi}{4}(0.15)^2(0.2) = 0.00353\ \text{m}^3
$$

#### (a) Volumetric efficiency
Pressure ratio $= 8$, $(8)^{1/1.3} = 4.951$.

$$
\eta_v = 1 + C - C\left(\frac{p_2}{p_1}\right)^{1/n} = 1 + 0.05 - 0.05 \times 4.951 = 0.8025
$$

#### (b) Air drawn per minute
Effective suction volume per cycle: $V_a = \eta_v V_s = 0.8025 \times 0.00353 = 0.00284$ m³.

One suction per revolution (single-acting):

$$
V = V_a N = 0.00284 \times 300 = 0.851\ \text{m}^3/\text{min}
$$

#### (c) Indicated power
$(p_2/p_1)^{\frac{n-1}{n}} = 8^{0.2308} = 1.6159$ and $p_1V_1 = 100 \times 0.851/60$ kW.

$$
P = \frac{1.3}{0.3} \times \frac{100 \times 0.851}{60} \times (1.6159 - 1) = 3.78\ \text{kW}
$$

(The clearance air is compressed and re-expands over the same index, so only the effective volume $V_a$ is used in the work formula.)

**Answer:** (a) 80.3 %; (b) 0.851 m³/min; (c) about 3.78 kW.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the volumetric efficiency?
   A. About 80.3 %
   B. About 95 %
   C. About 62 %
   D. About 100 %
   Answer: A. eta_v = 1 + 0.05 - 0.05 x 4.951 = 0.8025. (Key point: Volumetric efficiency)

2. Air drawn per minute for a single-acting compressor at 300 rpm is
   A. Vs x N x 2 = 2.12 m3/min
   B. eta_v x Vs x N = about 0.851 m3/min
   C. Vs x N = 1.06 m3/min
   D. Vs x 300 x 60
   Answer: B. Single-acting means one suction per revolution; 0.00284 x 300 = 0.851 m3/min. (Key point: Suction per minute)

3. Which volume is used in the indicated-power formula?
   A. The full swept volume only
   B. The clearance volume only
   C. The effective suction volume Va, because clearance air re-expands over the same index
   D. The volume at delivery
   Answer: C. Clearance work cancels, so only the effective volume drawn enters the work formula. (Key point: Volume for power)

4. What is the indicated power?
   A. About 7.5 kW
   B. About 0.5 kW
   C. About 14 kW
   D. About 3.78 kW
   Answer: D. P = (1.3/0.3)(100 x 0.851/60)(1.6159 - 1) = 3.78 kW. (Key point: Power value)

## Related in Applied Thermodynamics

- [Work of single-stage compressor without clearance](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Asingle-stage-compressor-work-derivation) — Applied Thermodynamics, chapter 2
- [Single-stage compressor power numerical](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Asingle-stage-compressor-numerical) — Applied Thermodynamics, chapter 2
- [Two-stage compressor with perfect intercooling](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Atwo-stage-compressor-intercooling-numerical) — Applied Thermodynamics, chapter 2
- [Components of reciprocating air compressor](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Areciprocating-compressor-components) — Applied Thermodynamics, chapter 2
- [Properties of moist air numerical](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Apsychrometric-properties-numerical) — Applied Thermodynamics, chapter 4
- [Effect of clearance and volumetric efficiency](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aclearance-volumetric-efficiency-derivation) — Applied Thermodynamics, chapter 2

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