---
title: "Engine test: four-cylinder, 85% mechanical efficiency"
subject: "Power Plant Equipment"
chapter: 5
key: "semester_7/power_plant_equipment:engine-test-85-percent"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/engine-test-85-percent
site: BCT Engineering
---

# Engine test: four-cylinder, 85% mechanical efficiency

Power Plant Equipment · Chapter 5: Diesel Power Plant

- Asked in: 2069 Chaitra, 8 marks
- Video: [IC Engine Performance | Numerical | 2021 | GTU Question Paper | Applied Thermodynamic | 3161910](https://www.youtube.com/watch?v=Kt1YJ7bYijk) — krunal khiraiya
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/engine-test-85-percent
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-5

## Question

In a test for four-cylinders, four-stroke engine has a diameter of 120 mm, stroke = 150 mm, speed of engine = 1800 rpm, fuel consumption of 0.25 kg/min, calorific value of fuel is 44000 kJ/kg. Difference in tension on either side of brake pulley = 40 kg, Brake circumference is 300 cm. If the mechanical efficiency is 85 %. Determine (a) Brake-thermal efficiency, (b) Indicated thermal efficiency, (c) Indicated mean effective pressure and (d) Brake specific fuel consumption.

## Short answer

Brake thermal efficiency = 19.26%, indicated thermal efficiency = 22.66%, imep = 4.08 bar, bsfc = 0.425 kg/kWh.

## Answer

**Data:** 4 cylinders, four-stroke, $D = 0.12$ m, $L = 0.15$ m, $N = 1800$ rpm, $\dot m_f = 0.25$ kg/min, CV = 44 000 kJ/kg, net tension = 40 kgf, brake circumference = 3.0 m (taken as the effective circumference, no rope size given), $\eta_m = 0.85$.

#### Brake and indicated power
$$
\begin{aligned}
F &= 40 \times 9.81 = 392.4\ \text{N},\quad R = \frac{3.0}{2\pi} = 0.4775\ \text{m} \\
BP &= \frac{2\pi N F R}{60} = 392.4 \times \frac{3.0 \times 1800}{60} = 35\,316\ \text{W} = 35.316\ \text{kW} \\
IP &= \frac{BP}{\eta_m} = \frac{35.316}{0.85} = 41.548\ \text{kW}
\end{aligned}
$$
Heat supplied:
$$
\dot Q = \frac{0.25}{60}\times 44\,000 = 183.33\ \text{kW}
$$

#### (a) Brake thermal efficiency
$$
\eta_{bth} = \frac{35.316}{183.33} = 0.1926 = 19.26\%
$$

#### (b) Indicated thermal efficiency
$$
\eta_{ith} = \frac{41.548}{183.33} = 0.2266 = 22.66\%
$$

#### (c) Indicated mean effective pressure
$$
\begin{aligned}
A &= \frac{\pi}{4}(0.12)^2 = 0.011310\ \text{m}^2,\quad n = \frac{N}{2} = 900,\ k = 4 \\
p_{mi} &= \frac{60\,IP}{L A n k} = \frac{60 \times 41\,548}{0.15 \times 0.011310 \times 900 \times 4} \\
&= 4.082\times10^5\ \text{N/m}^2 = 4.08\ \text{bar}
\end{aligned}
$$

#### (d) Brake specific fuel consumption
$$
bsfc = \frac{0.25 \times 60}{35.316} = \frac{15}{35.316} = 0.4247\ \text{kg/kWh}
$$

**Answer:** $\eta_{bth}$ = 19.26 %, $\eta_{ith}$ = 22.66 %, imep = 4.08 bar, bsfc = 0.425 kg/kWh.

## Check yourself

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

1. BP is found from net tension and circumference as
   A. 40 x 3.0 x 1800
   B. 392.4 x 3.0 /60
   C. 40 x 1800/60
   D. 392.4 N x (3.0 m x 1800/60) = 35.3 kW
   Answer: D. 40 kgf = 392.4 N; distance per second = 90 m. (Key point: Brake power)

2. Heat supplied for 0.25 kg/min at 44000 kJ/kg
   A. 183.33 kW
   B. 11000 kW
   C. 3.06 kW
   D. 660 kW
   Answer: A. 0.25/60 kg/s x 44000 = 183.33 kW. (Key point: Heat supplied)

3. Which pair is correct?
   A. eta_bth = IP/Q; eta_ith = BP/Q
   B. eta_bth = BP/Q = 19.26%; eta_ith = IP/Q = 22.66%
   C. Both equal BP/Q
   D. eta_ith = BP/IP
   Answer: B. Indicated thermal efficiency is higher since IP = BP/0.85 > BP. (Key point: Thermal efficiencies)

4. Which values are used in imep = 60 IP/(L A n k)?
   A. n = 1800, k = 4
   B. n = 900, k = 1, BP
   C. n = 900, k = 4, IP = 41.55 kW
   D. n = 3600, k = 4
   Answer: C. Four-stroke: n = N/2; four cylinders; indicated power gives 4.08 bar. (Key point: imep)

## Close variants set in other exams

- [Engine test: four-cylinder at 1820 rpm](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-1820-rpm) — Power Plant Equipment, chapter 5, asked 5×
- [Engine test: four-cylinder at 1800 rpm](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-1800-rpm) — Power Plant Equipment, chapter 5, asked 5×
- [Engine test: four-cylinder with rope radius](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-rope-radius) — Power Plant Equipment, chapter 5, asked 5×
- [Engine test: four-cylinder at 2000 rpm](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-2000-rpm) — Power Plant Equipment, chapter 5, asked 5×

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- [Engine test: 4-cylinder, B.P. 31.4 kW](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aengine-test-bp-31-4kw) — Power Plant Equipment, chapter 5, asked 2×
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- [Single cylinder engine: 60-minute trial](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Asingle-cylinder-60-min-trial) — Power Plant Equipment, chapter 5, asked 2×
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