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Qwestrum Engineering360 · Mechanical Engineering · Applied Thermodynamics

Internal Combustion Engines

Engine performance is measured by brake power BP = 2πNT/60, brake thermal efficiency η = BP/(ṁ_f·CV), and specific fuel consumption SFC = ṁ_f/BP. Mechanical efficiency links brake and indicated power, per P.K. Nag.
Exam tip: lock the sign convention (Q into system, W by system in P.K. Nag) before substituting; use absolute temperature for ideal-gas and efficiency ratios.

Key formulas & points

Skim these first — then read the full notes below.

  • Volumetricefficiencyηv=mactualmtheoreticalVolumetric efficiency \eta_{v} = \frac{m_{actual}}{m_{theoretical}}
  • Mechanical efficiency = BP/IP
  • Morite testing: IP from indicator diagram area

Topic details

Introduction

IC-engine performance testing is a practical topic in Indian applied-thermo courses, examined through Morse tests, heat balance sheets, and efficiency calculations. P.K. Nag defines indicated, brake, and friction power and the efficiencies relating them.

Scope in B.Tech and GATE syllabus

Indicated power comes from the indicator diagram (IMEP × swept volume × cycles); brake power is measured at the shaft with a dynamometer; friction power is the difference. Mechanical efficiency = BP/IP.

Why this topic matters in practice

Volumetric efficiency measures breathing (actual vs theoretical air induction), and brake thermal efficiency measures fuel-energy conversion. Distinguishing these efficiencies and applying the correct one to the asked quantity is what earns marks; mixing indicated and brake quantities is the usual pitfall.

Key relations & formulas

ηbrake=BP(mf×CV)\eta_{brake} = \frac{BP}{(mf \times CV)}
(brake thermal efficiency)
BP=(2πNT)(60×1000)kWBP = \frac{(2\pi NT)}{(60 \times 1000)} kW
(T in N·m, N in rpm)
SFC=mfBPSFC = \frac{mf}{BP}
(specific fuel consumption, kg/kWh)
IMEP=(n⋅Wnet)(Vswept)IMEP = \frac{(n\cdot W_{net})}{(V_{swept})}
(indicated mean effective pressure)

Notation and sign conventions

Relation 1 —
ηbrake=BP/\eta_{brake} = BP/
ηbrake=BP(mf×CV)\eta_{brake} = \frac{BP}{(mf \times CV)}
(brake thermal efficiency)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
BP=BP =
BP=(2πNT)(60×1000)kWBP = \frac{(2\pi NT)}{(60 \times 1000)} kW
(T in N·m, N in rpm)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
SFC=mfBPSFC = \frac{mf}{BP}
SFC=mfBPSFC = \frac{mf}{BP}
(specific fuel consumption, kg/kWh)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
IMEP=IMEP =
IMEP=(n⋅Wnet)(Vswept)IMEP = \frac{(n\cdot W_{net})}{(V_{swept})}
(indicated mean effective pressure)
Write this relation with symbols exactly as in Engineering Thermodynamics — P.K. Nag before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Fundamentals and definitions

Brake power is the useful shaft output: BP = 2πNT/60 with torque T in N·m and speed N in rev/s (or ÷60 for rpm). Indicated power IP = IMEP × L × A × n comes from the in-cylinder pressure work; friction power FP = IP − BP.

Governing relations in practice

Mechanical efficiency η_mech = BP/IP quantifies losses in bearings and pumping. It falls at part load because friction is roughly constant while output drops.

Design and analysis considerations

Brake thermal efficiency η_bth = BP/(ṁ_f·CV) is the fraction of fuel calorific value converted to shaft work; indicated thermal efficiency uses IP instead. Specific fuel consumption SFC = ṁ_f/BP (kg/kWh) is the inverse practical measure.

Advanced theory and extensions

Volumetric efficiency η_v = actual air mass/theoretical (swept-volume) air mass reflects how well the engine breathes; turbocharging raises it above one. A heat balance sheet then accounts for fuel energy split between brake work, cooling, exhaust, and radiation — the complete performance picture.

Assumptions and validity limits

State assumptions explicitly before using any relation for internal combustion engines — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Applied Thermodynamics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Applied Thermodynamics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to internal combustion engines.
4. Use equation 1:
ηbrake=BP/\eta_{brake} = BP/
.
5. Use equation 2:
BP=BP =
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Internal Combustion Engines appears in IC engines, gas turbines, and compressors. In Indian mechanical curricula this topic is tested because it connects theory to air-standard and vapour power cycles.
GATE and semester exams often combine internal combustion engines with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use internal combustion engines?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

• Confusing indicated power with brake power in efficiency calculations
• Using N in rpm without converting when the formula expects rev/s
• Mixing brake thermal efficiency with mechanical efficiency
• Forgetting to convert calorific value units (kJ/kg) consistently with fuel flow rate

Quick revision checklist

Before attempting internal combustion engines problems, confirm you can:
1.
Volumetricefficiencyηv=mactualmtheoreticalVolumetric efficiency \eta_{v} = \frac{m_{actual}}{m_{theoretical}}

2. Mechanical efficiency = BP/IP
3. Morite testing: IP from indicator diagram area
Revise the solved examples in Engineering Thermodynamics — P.K. Nag and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Brake power of an engine

Problem

An engine develops a torque T = 200 N·m at N = 1500 rpm. Find the brake power.

Solution

BP = 2πNT/60 = 2π × 1500 × 200/60 = 6.283 × 25 × 200 = 31416 W ≈ 31.4 kW.

Conceptual check — Internal Combustion Engines

Problem

In a Applied Thermodynamics semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of internal combustion engines." What should a complete answer include?

Practice questions

Most-asked interview and GATE questions for this topic — expand any item for a model answer.

  1. 1
    What is Internal Combustion Engines, and why does it appear in B.Tech / GATE syllabi?

    Model answer

    Engine performance is measured by brake power BP = 2πNT/60, brake thermal efficiency η = BP/(ṁ_f·CV), and specific fuel consumption SFC = ṁ_f/BP. Mechanical efficiency links brake and indicated power, per P.K. Nag.
  2. 2
    State the relation η_brake = BP/ and name each symbol.

    Model answer

    The governing relation is ηbrake=BP/\eta_{brake} = BP/. Write every symbol with SI units before substituting numbers.
  3. 3
    State the relation BP = and name each symbol.

    Model answer

    The governing relation is BP=BP =. Write every symbol with SI units before substituting numbers.
  4. 4
    State the relation SFC = mf/BP and name each symbol.

    Model answer

    The governing relation is SFC=mfBPSFC = \frac{mf}{BP}. Write every symbol with SI units before substituting numbers.
  5. 5
    State the relation IMEP = and name each symbol.

    Model answer

    The governing relation is IMEP=IMEP =. Write every symbol with SI units before substituting numbers.
  6. 6
    Explain: Volumetric efficiency η_v = m_actual/m_theoretical

    Model answer

    Volumetricefficiencyηv=mactualmtheoreticalVolumetric efficiency \eta_{v} = \frac{m_{actual}}{m_{theoretical}} — state the assumption range and one exam trap linked to this point.
  7. 7
    Explain: Mechanical efficiency = BP/IP

    Model answer

    Mechanical efficiency = BP/IP — state the assumption range and one exam trap linked to this point.
  8. 8
    Explain: Morite testing: IP from indicator diagram area

    Model answer

    Morite testing: IP from indicator diagram area — state the assumption range and one exam trap linked to this point.
  9. 9
    How would you correct this error in a viva: Confusing indicated power with brake power in efficiency calculations?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  10. 10
    How would you correct this error in a viva: Using N in rpm without converting when the formula expects rev/s?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  11. 11
    How would you correct this error in a viva: Mixing brake thermal efficiency with mechanical efficiency?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
  12. 12
    How would you correct this error in a viva: Forgetting to convert calorific value units (kJ/kg) consistently with fuel flow rate?

    Model answer

    Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.

Exams & GATE

  • 1
    P.K. Nag Ch. 17 — distinguish indicated, brake, and mechanical efficiency.
  • 2
    Avoid: Confusing indicated power with brake power in efficiency calculations
  • 3
    Avoid: Using N in rpm without converting when the formula expects rev/s
  • 4
    Avoid: Mixing brake thermal efficiency with mechanical efficiency

📖 Standard books (India)

  • Engineering Thermodynamics — P.K. Nag

    Read: Syllabus unit

    The standard thermodynamics text in most Indian universities

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