APPLIED THERMODYNAMICS 18ME42 Module 01 question no 2a &2b

Mr THANMAY J S, Asst Proff, Dept of Mechanical Engineering, VVIET Mysore Page 1
APPLIED THERMODYNAMICS
18ME42
Course Coordinator
Mr. THANMAY J. S
Assistant Professor
Department of Mechanical Engineering
VVIET Mysore
Module 01: Question Number 2a & 2b: I C Engines
Course Learning Objectives
 To understand fundamentals of I. C. Engines, Construction and working Principle of an
Engine and Compare Actual, Fuel-Air and Air standard cycle Performance.
 To study Combustion in SI and CI engines and its controlling factor in order to extract
maximum power.
 To know the concepts of testing of I. C. Engines and methods to estimate Indicated, Brake
and Frictional Power and efficiencies.
Course Outcomes
At the end of the course the student will be able to:
CO2: Understand combustion of fuels and performance of I C engines.

CONTENT
2.0 I.C. Engines.
2.1 Classification of IC engines.
2.2 Combustion of SI engine.
2.3 Combustion of CI engine.
2.4 Detonation and factors affecting detonation.
2.5 IC Engine fuels,
2.6 Ratings of SI Engine Fuels
2.7 Ratings of CI Engine Fuels
2.8 Alternate Fuels.
2.9 Performance analysis of I.C Engines.
2.10 Heat balance.
2.11 Morse test.

2.0 I.C. Engines
An Engine is a Device which transforms one form of energy into another form of Energy.
(Reciprocation motion to Rotary motion)
The following terms and abbreviations are commonly used in engine technology literature.
Internal Combustion (I C) or Spark Ignition (S I): An engine in which the combustion
process in each cycle is started by use of a spark plug.
Compression Ignition (C I): An engine in which the combustion process starts when the air-
fuel mixture self-ignites due to high temperature in the combustion chamber caused by high
compression pressure. CI engines are often called Diesel engines,
IC engine Nomenclature
The following terms/Nomenclature associated with an engine are explained for the better
understanding of the working principle of the Internal Combustion engines
1. Bore
2. Piston Area
3. Stroke
4. Top Dead Center
5. Bottom Dead Center
6. Clearance Volume
7. Swept Volume
8. Compression Ratio
9. Mean Effective Pressure
10. Combustion chamber
1. Bore
The nominal inside diameter of the engine cylinder is called Cylinder bore. Designate by
the Letter d and expressed in millimeters (mm)
2. Piston Area
The area of the circle of diameter equal to the cylinder bore is called the Piston
Area. Designate by the Letter A and expressed in square centimeters (cm²) or square
millimeters (mm2
) A = πd²/4
3. Stroke
The maximum distance travelled by the piston in the cylinder in one direction is known as
stroke. In other words, the distance travelled by the piston from TDC to BDC is called the
stroke. Designate by the Letter L and expressed in in millimeters (mm)

4. Top Dead Center
The extreme position of the piston at the top of the cylinder of the vertical engine is called
the top dead center (TDC).
5. Bottom Dead Center
The extreme position of the piston at the bottom of the cylinder of the vertical engine called
bottom dead center (BDC).
6. Clearance Volume
The volume contained in the cylinder above the top of the piston, when the piston is at the
top dead center is called the clearance volume. Designate by the Letter Vc and expressed in
in cubic centimeters (cc)
7. Swept Volume
Swept volume is the volume covered by the piston while moving from TDC to BDC. In
other words, the volume swept by the piston during one stroke is called the swept volume
or piston displacement.
Swept Volume (Vs) = Vs = A x L
8. Compression Ratio
Compression ratio is a ratio of the volume when the piston is at the bottom dead center to
the volume when the piston is at top dead center.
Compression ratio =
Maximum Cylinder Volume
Minimum Cylinder Volume
=
(Swept Volume + Clearance Volume)
Clearance Volume
𝐂𝐨𝐦𝐩𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐫𝐚𝐭𝐢𝐨 =
𝑽𝒔 + 𝑽𝒄
𝑽𝒄
usually, the compression ratio will vary from 5: 1 to 10: 1 for petrol engines and from 12:1
to 22: 1 for diesel engines.
9. Mean Effective Pressure
This is the Average pressure acting on the piston during the thermodynamic processes.
Mean Effective Pressure =
Torque × Number of revolution for the power stroke × 2π
Displacement
10. Combustion Chamber
The space enclosed in the upper part of the cylinder, by the cylinder head and the piston top
(TDC) during the combustion process, is called the combustion chamber. Combustion chamber
is the closed space in which combustion of fuel takes place.

2.1 Classification of IC engines
Sl.No Classification Criteria Classification or Types
1 No of Strokes per cycle
1. Four Stroke Engine
2. Two Stroke Engine
2 Types of Fuel Used
1. Petrol or Gasoline Engine
2. Diesel Engine
3. Gas Engine
4. Bi-Fuel Engine
3
Nature of Thermodynamic
Cycle
1. Otto Cycle Engine
2. Diesel Cycle Engine
3. Dual Combustion Cycle Engine
4 Method of Ignition
1. Spark Ignition (SI) Engine
2. Compression Ignition (CI) Engine
5 No of Cylinders
1. Single Cylinder Engine
2. Multi Cylinder Engine
6 Arrangement of Cylinders
1. Horizontal Engine
2. Vertical Engine
3. V – Type Engine
4. Radial Engine
5. Inline Engine
6. Opposed Cylinder Engine
7. Opposed Piston Engine
7 Cooling System
1. Air Cooled Engine
2. Water Cooled Engine
8 Lubrication System
1. Wet Sump Lubrication System
2. Dry Sump Lubrication System
9 Speed of the Engine.
1. Slow Speed Engine
2. Medium Speed Engine
3. High Speed Engine
10 Location of Valves
1. Over Head Valve Engine
2. Side Valve Engine

2.2 Combustion of SI engine
As you can see the combustion process will be completed in the three stages in an actual engine.
1. Ignition Lag
2. Flame Propagation
3. After burning
Pressure vs Crank angle diagram [p-θ Diagram]
1. Ignition Lag
The time interval between the passage of the spark and the inflammation of the air-fuel mixture
is known as ignition lag or Ignition delay. It is also referred to as the preparation phase.
There are two chances that can cause the ignition delay. Physical delay and chemical delay.
Physical delay due to the atomization, vaporization and mixing of air fuel. The chemical delay
due to pre-combustion reactions. The ignition lag depends on the heat, pressure, the nature of
the fuel and the proportion of the exhaust gas residuals.
2. Flame Propagation
The flame propagation means that the propagation of combustion waves through a combustible
mixture. Or simply the spread of the flame throughout the combustion chamber. When the
ignition initiated, the adjacent layer of the reaction zone also ignites and propagated to the next
layer. This continued throughout the mixture in the combustion chamber. This process takes
some time to spread the flame throughout the combustion chamber. During this stage the
pressure rises with very little change in the volume. But it cannot be instantaneous as we
claimed to be in the actual cycle.
3. After burning
This After Burning stage begins where the cylinder pressure reaches a maximum point(c) in
the cylinder. Also, flame propagation gradually decreases due to the flame velocity will reduce.
The expansion stroke will start at or before this stage. so there will be no pressure rise in this
stage.

2.3 Combustion of CI engine
In the Combustion Ignition Engine, the combustion process will be completed in the four stages
in an actual engine.
1. Ignition Lag
2. Rapid Combustion
3. Controlled Combustion
4. After Burning
Combustion Ignition Engine Pressure vs Crank angle diagram [p-θ Diagram]
1. Ignition Lag
The time interval between the injection of the fuel and the start of the self-ignition of the fuel
is known as ignition lag or Ignition delay. It is also referred to as the preparation phase.
The fuel does not ignite immediately upon the injection of fuel into the combustion chamber.
There will be a definitely a certain amount of period will be delayed between the first droplet
of the fuel injected into the combustion chamber and the time at which it starts the burning
phase.
There are two chances that can cause the ignition delay. Physical delay and chemical delay.
Physical delay due to the complete injection of fuel, atomization, vaporization and mixing of
air and fuel and raised to its self-ignition point. The chemical delay due to the burning slowly
starts and then accelerates until the complete ignition takes place.
2. Rapid Combustion
The period of rapid combustion also known as the uncontrolled combustion. This rapid
combustion will start right After the ignition delay period ends. During this period the heat
release is maximum.
The pressure released during this period depends on the ignition delay period. If the ignition
delay period is more, then the pressure rise is more due to the more fuel will be accumulated
during the delay period.

3. Controlled Combustion
The rapid combustion followed by the third stage called the controlled combustion. During the
rapid combustion, the cycle reaches its maximum pressure and the temperature. Which means
the fuel droplets injected into the combustion chamber during the rapid combustion stage will
burn faster with reduced ignition delay as soon as they find the necessary oxygen and any
further pressure rise is controlled by the injection.
At the point at where it reaches the maximum cycle pressure the rapid combustion ends and
the controlled combustion starts. The period of the controlled combustion is assumed to end at
the maximum cycle temperature
4. After Burning
The combustion process will not stop right after the completion of the injection process. The
unburnt particles left in the combustion particles will start burning as soon as they get in contact
with the oxygen. This process continued for a certain period amount of time called the after
burning.
2.4 Detonation and factors affecting detonation
Engine detonation is an engine refers to inappropriate combustion of fuel in the combustion
chamber/cylinder of the engine. Either the compressed air fuel mixture is burnt in the cylinders
with help of a spark (in SI petrol engines) or the air alone is compressed during the compression
stroke and fuel is injected and burnt due to compression (in CI diesel engines).

Engine detonation can also be illustrated as it can also occur due to sudden and instantaneous
ignition of the unburnt charge when the temperature and pressure is so high and sufficient to
ignite the fuel or air fuel mixture. The factors affecting engine detonation can be classified as
follows:
1. Engine factors
2. Air, Fuel and Air-Fuel mixture factors
1. Engine factors
There are engine characteristics which can affect engine detonation include:
a) Compression ratio: Engine detonation increases with increase in compression ratio as it
increases the gas temperature and pressure thus lowering the reaction time for charge to get
ignited. Every engine is designed for a particular maximum compression ratio and any
compression ratio beyond this, causes engine detonation.
b) Engine size: Engine detonation increases with increase in cylinder size (bore).
c) Spark advance: Retarded spark helps in lowering the detonation whereas over-advance in
spark leads to more detonation as pressure gets higher than the normal maximum pressure.
d) Design of combustion chamber: The design which produces more turbulence in the
combustion chamber, it helps in rapid combustion of the charge and hence decrease the
chances to knock or detonate.
e) Defective cooling system: If engine cooling system is not working properly due to fault in
engine thermostat, water pump etc., it can also increase the engine detonation.
f) Engine speed: At higher engine speeds which may also lead to fall in volumetric
efficiency, the engine detonation is decreased.
g) Valve timing: As the valve timing increases the volumetric efficiency which increases the
air-fuel mixture intake and increase the cylinder pressure, the tendency to engine detonation
is also increased.
2. Air, Fuel and Air-Fuel Mixture factors
It has been observed that charge characteristics mentioned below can also be significant factors
which can cause engine detonation. - Octane number
Effects of detonation Prevention of Detonation
1. Inefficient combustion.
2. Loss power.
3. Local overheating.
4. Mechanical engine failure.
1. Anti-knock agents.
2. Cooling of the charge.
3. Reducing the time factor.

2.5 IC Engine fuels.
Important qualities of SI engine fuels Important qualities of CI engine fuels
1. Volatility Front End Volatility (0-
20%)
• Cold Starting • Hot Starting
(Percolation)
• Vapor Lock
• Evaporative loss Mid-Range Volatility
(20-80%)
• Warmup
• Short and Long trip economy
• Acceleration, Smoothness
• Carburetor Icing Tail End Volatility
(80-100%)
• Crankcase dilution
• Deposits & Spark plug Fouling
2. Anti-Knock Quality Depends on
chemical composition and molecular
structure. High compression ratios can
be employed with high anti knocking
quality.
3. Gum Content Reactive HCs and
impurities tend to oxidize upon storage
forming sticky substances (liquid &
solid). Sticking valves/pistons, clogging
of carburetor, carbon deposits etc. Least
is desirable.
4. Sulphur Content May contain free
Sulphur, hydrogen supplied and other
Sulphur compounds which increases
corrosive nature of fuel. Also harmful
emissions, increased knocking tendency
etc. Least is desirable.
A. Satisfactory handling & storage
1. Flash and fire points: indicates the temperature below
which oil can be handled without danger of fire.
2. Viscosity: should be low enough for easy pumping and
high enough to provide some lubrication.
3. Cloud point: The temperature below which the wax
content separates out as solid is called cloud point. This
waxy solid can clog fuel lines and filters. This should be
low.
4. Pour point: The temperature below which the fuel freezes
making flow impossible. This should be low.
B. Smooth and efficient burning
1. Volatility: should be high for proper mixing, burning and
starting characteristics. Lower volatility → less fuel boil off
from injector → less HC emissions. Lower volatility → less
NOx emissions. High volatility also slightly affects smoke
density and odor of exhaust.
2. Ignition delay: too long → high knocking. Too short →
smoke due to insufficient mixing.
3. Anti-knock characteristics: should be good.
4. Specific gravity: should be high → in density.
5. Heat of combustion: should be high.
C. Continued cleanliness during usage
1. Contamination: sand/rust/abrasive particles/ice can clog
or damage parts.
2. Sulphur: causes corrosion, wear, sludge/sticky deposits.

2.6 Rating of SI Engines Fuels
OCTANE Number
• Knock quality is rated by comparing with Primary Reference Fuels (PRF)
1. Iso-octane, C8H18 (2-2-4- trimethyl pentane) …….O.N. – 100
2. n-heptane, C7H16 …….O.N. – 0
• The % by volume of Iso-octane in a mixture of isooctane and n- heptane which exactly
matches the knocking intensity of the test fuel in a standard engine under a set of standard
operating conditions is defined as the Octane Number.
• Cooperative Fuel Research Engine (CFR); 900 rpm, 38 0C Intake T, Coolant temperature 100
0C, Ignition advance 13 BTDC
2.7 Rating of CI Engines Fuels
CETANE Number
• Knock quality is rated by comparing with Primary Reference Fuels (PRF)
• n-cetane, C16H34 …….C.N. – 100
• Alpha methyl naphthalene, C11H10 …….C.N. – 0
• The % by volume of n-cetane in a mixture of n-cetane and Alpha methyl naphthalene which
has the same ignition characteristics (ignition delay) as the test fuel in a standard engine under
specified operating conditions is defined as Cetane Number.
• Cooperative Fuel Research Diesel Engine (CFR); 900 rpm, 65.5 0C Intake T, Coolant
temperature 100 0C, injection advance 130 bTDC, ignition delay 130.
2.8 Alternate Fuels.
Fuels Resource
Expended energy
[MJ/MJ fuel]
Greenhouse emissions
[g CO2/MJ]
Gasoline Crude oil 0.18 13.8
Diesel Crude oil 0.20 15.4
Natural gas
EU-mix NG 0.17 13.0
Imported NG 7000 km 0.29 22.6
LNG* 0.28 19.9
Shale gas 0.10 7.8
Ethanol
Sugar* 1.20 28.4
Wheat* 1.31 55.6
Other* 1.66 41.4
Hydrogen
Natural Gas* 1.10 118
Coal* 1.45 237
Biomass* 1.05 14.6
Electricity* 3.11 190

2.9 Performance analysis of I.C Engines.
i) Indicated Mean Effective Pressure
It can be defined as the average pressure
developed inside the cylinder of an IC
engine. It is calculated using the equation,
𝑃𝑚 =
𝑆 × 𝑎
𝑙
Where,
S = Spring Value of the Spring used in the
Indicator;
a = Area of the Indicator Diagram;
l = Length of the Indicator Diagram
ii) Indicated Power
It can be defined as the total power developed inside
the engine cylinder due to combustion of fuel. It is
given by,
𝐼𝑃 =
𝑛 𝑃𝑚 𝐿𝐴𝑁𝐾
(
60
1000
)
𝑜𝑟
𝑰𝑷 = 𝒏 𝑷𝒎 𝑳𝑨𝑵𝑲 (
𝟏𝟎
𝟔
)
Where,
IP = Indicated Power in KW;
n = No. of Cylinders;
L = Stroke in m;
A = Piston Area in m2;
N = Engine Speed in rpm;
K = 1 for 2S engine and ½ for 4S engine.
iii) The brake power (briefly written as B.P) of an IC Engine is the power available at the
crankshaft.
𝐵. 𝑃 =
𝐴𝑛𝑔𝑙𝑒 𝑡𝑢𝑟𝑛𝑒𝑑 𝑖𝑛 𝑟𝑎𝑑𝑖𝑎𝑛𝑠 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 1 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 × 𝑇𝑜𝑟𝑞𝑢𝑒 𝑖𝑛 𝑁. 𝑚
60
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
= 𝐾𝑖𝑙𝑜 𝑤𝑎𝑡𝑡𝑠
Torque (T) Calculation using Brake Drum
Dynamometer
Effective radius of the brake R = (D+ d)/2
Brake load or net load = (W-S) in Newton
Braking
D= dia. Of drum
d = rope dia.
S = spring balance reading
Torque = T = (W-S)×R in N-m
iv) Friction Power:
Friction power is the power lost during transmission from inside the cylinder (indicated power) to
the shaft (brake power); FP = IP − BP

v) Mechanical Efficiency
𝜼(𝒎𝒆𝒄𝒉) =
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Thermal Efficiency
𝜂(𝑡ℎ) =
𝑃𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡
𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑
× 100
𝑤ℎ𝑒𝑟𝑒 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 = 𝑚𝑓 × 𝐶𝑣
mf = mass of fuel supplied kg/sec
Cv = calorific value of the fuel KJ/kg
vi) Indicated Thermal Efficiency
𝜼(𝒕𝒉) =
𝑰𝑷
𝒎𝒇 × 𝑪𝒗
× 𝟏𝟎𝟎
vii) Brake Thermal Efficiency
𝜼(𝒕𝒉) =
𝑩𝑷
× 𝟏𝟎𝟎
Specific Fuel consumption
𝑆𝐹𝐶 =
𝐹𝑢𝑒𝑙 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑑(𝑚𝑓) (
𝑘𝑔
ℎ𝑟
)
𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 (𝑘𝑤)
× 100
In Kg/kW-hr
viii) Indicated Specific Fuel consumption
𝑺𝑭𝑪 =
𝑭𝒖𝒆𝒍 𝑺𝒖𝒑𝒑𝒍𝒊𝒆𝒅(𝒎𝒇)
𝑰𝑷 (𝒊𝒏 𝒌𝒘)
× 𝟏𝟎𝟎
ix) Brake Specific Fuel consumption
𝑺𝑭𝑪 =
𝑩𝑷 (𝒊𝒏 𝒌𝒘)
× 𝟏𝟎𝟎
x) Piston speed = 2 L N
L = Stroke Length
N= Engine speed

2.10 Heat balance sheet of I C Engine
Heat Balance Sheet is an account of heat supplied and heat utilized in various ways in
the IC engine. Heat balance sheet is used to get necessary information regarding the
performance of IC Engine. Heat balance sheet can be done on second basis or minute basis
or hour basis. Since heat balance sheet is account of heat supplied and heat utilized by
engine. So we should keep list of heat supplied to engine and heat utilized by engine.
The heat supplied to engine is only by combustion of fuel and is equal to :-
(𝐴) = 𝑸𝒔 = 𝒎𝒇 × 𝑪𝒗 𝐾𝐽/𝑚𝑖𝑛
Where, mf = mass of fuel used in kg/min
Cv = Calorific value of fuel in KJ/kg
List of heat which are utilized by the engines are:
1) Heat equivalent to brake power of engine or Heat lost in producing useful power QBP
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝒐𝒏 𝒎𝒊𝒏𝒖𝒕𝒆 𝒃𝒂𝒔𝒊𝒔: 𝑸𝑩𝑷 = 𝑩. 𝑷 × 𝟔𝟎 𝐾𝐽 /𝑚𝑖𝑛
𝒐𝒏 𝒑𝒆𝒓𝒄𝒆𝒏𝒕𝒂𝒈𝒆(%) 𝒃𝒂𝒔𝒊𝒔: =
𝑸𝑩𝑷
𝑸𝑺
× 𝟏𝟎𝟎
2) Heat carried away by cooling water.
𝑸𝒘 = 𝒎𝒘 × 𝑪𝑷𝑾×[𝑻𝑾𝑶𝑼𝑻 − 𝑻𝑾𝑰𝑵] 𝐾𝐽 /𝑚𝑖𝑛
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑜𝑓 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑤𝑎𝑡𝑒𝑟 𝑪𝑷𝑾 = 4.187 𝐾𝐽 /𝑘𝑔𝐾
𝑸𝑾
𝑸𝑺
× 𝟏𝟎𝟎
3) Heat exhausted with the exhaust gases
𝑸𝒈 = 𝒎𝒆𝒙𝒉 × 𝑪𝑷𝒈 × [𝑻𝑬𝒙𝒉 − 𝑻𝒓𝒐𝒐𝒎] 𝐾𝐽 /𝑚𝑖𝑛
𝑤ℎ𝑒𝑟𝑒 𝑚𝑒𝑥ℎ = 𝑚𝑎 + 𝑚𝑓 = [
𝑚𝑎
𝑚𝑓
+ 1] 𝑘𝑔/ min [
𝑚𝑎
𝑚𝑓
] =
𝐴𝑖𝑟
𝐹𝑢𝑒𝑙
𝑟𝑎𝑡𝑖𝑜
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑜𝑓 𝑒𝑥ℎ𝑎𝑜𝑢𝑠𝑡 𝑔𝑎𝑠 𝑪𝑷𝒈 = = 1.005 KJ/kgK
𝑸𝒈
𝑸𝑺
× 𝟏𝟎𝟎
4) Unaccounted heat loss.
𝑸𝑼𝒏𝒂𝒄𝒄𝒐𝒖𝒏𝒕 = 𝑸𝒔 − (𝑸𝑩𝑷 + 𝑸𝑾 + 𝑸𝒈) 𝐾𝐽 /𝑚𝑖𝑛
𝑸𝑼𝒏𝒂𝒄𝒄𝒐𝒖𝒏𝒕
𝑸𝑺
× 𝟏𝟎𝟎

Now, we have values of heat supplied and heat utilized by the engine. From these values,
we have to prepare a balance sheet
The result of the different values of heat supplied and heat utilized are tabulated in a table
and this table is known Heat Balance Sheet. This table also has percentage representation of
heat supplied and heat utilized. Heat supplied has only one value and that is heat supplied by
fuel combustion which covers whole 100% of heat supplied. Heat utilized column has four
values heat in BP, heat carried away by cooling water, heat carried away by exhaust gases and
the rest of unaccounted heat. This four together meets to form 100% of utilized heat.
2.11 Morse test.
Morse test is a method to measure the frictional power of a multi-cylinder SI engine.
Morse Test – This test carried out on multi cylinder I.C. engine. In this test, first engine is
allowed to run at constant speed and brake power of engine is measured when all cylinders are
working and developing indicated power. (Considering Four cylinders)
IP1+IP2+IP3+IP4 = (BP)engine +(FP1+FP2+FP3+FP4)
 Where IP1, IP2, IP3 and IP4 – Indicated power of four cylinders
 (BP)engine – Brake power of engine when all cylinders are working
 FP1, FP2, FP3, FP4 – Frictional power of all four cylinders
Then the first cylinder is cut off by short circuiting spark plug in case S.I. engine (or cutting
fuel supply in case C.I. engine). This causes the speed to drop due to non-firing of first cylinder.
It should be noted that although first cylinder is not producing power still it is moving up and

down so its frictional power must be considered. This speed is once again maintained to its
original value by reducing load on the engine
IP2+IP3+IP4 = (BP)2,3,4 +(FP1+FP2+FP3+FP4)
Where (BP)2,3,4 – Brake power of 2,3 & 4 cylinders only.
Repeat the above procedure for remaining cylinders and calculate I.P. of the engine.
Cylinder 2 is cut off – IP1+IP3+IP4 = (BP)1,3,4 +(FP1+FP2+FP3+FP4)
I.P. of cylinder 1 is calculated as,
IP1 = (BP)engine – (BP)2,3,4
Similarly, IP2, IP3 and IP4 is calculated as follows
Total Indicated power of engine = I.P
IP = IP1+IP2+IP3+IP4
Frictional power of engine is,
FP = IP – (BP)engine
and mechanical efficiency is,
Mechanical Efficiency 𝜼 (𝒎𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍) =
𝑩𝑷𝒂𝒍𝒍
𝑰𝑷
× 𝟏𝟎𝟎
Thus Morse test is used to calculate IP, FP and mechanical efficiency by assuming FP of each
cylinder remains constant.

List of Formulas
𝐂𝐨𝐦𝐩𝐫𝐞𝐬𝐬𝐢𝐨𝐧 𝐫𝐚𝐭𝐢𝐨 =
𝑽𝒔 + 𝑽𝒄
𝑽𝒄
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑚𝑒𝑎𝑛 𝑒𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑷𝒎 =
𝑺 × 𝒂
𝒍
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟𝑰𝑷 = 𝒏 𝑷𝒎 𝑳𝑨𝑵𝑲 (
𝟏𝟎
𝟔
)
K = 1 for 2S engine and ½ for 4S engine
𝐵𝑟𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑟 𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
Friction power FP = IP − BP Torque = T = (W-S)×R in N-m
Mechanical Efficiency 𝜼(𝒎𝒆𝒄𝒉) =
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Thermal Efficiency
𝜂(𝑡ℎ) =
𝑃𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡
𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑
× 100
𝑤ℎ𝑒𝑟𝑒 𝐻𝑒𝑎𝑡 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 = 𝑚𝑓 × 𝐶𝑣
mf = mass of fuel supplied kg/sec
Cv = calorific value of the fuel KJ/kg
Indicated Thermal Efficiency
𝜼(𝒕𝒉) =
𝑰𝑷
× 𝟏𝟎𝟎
Brake Thermal Efficiency
𝜼(𝒕𝒉) =
𝑩𝑷
× 𝟏𝟎𝟎
Specific Fuel consumption
𝑆𝐹𝐶 =
𝐹𝑢𝑒𝑙 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑑(𝑚𝑓) (
𝑘𝑔
ℎ𝑟
)
𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 (𝑘𝑤)
× 100
In Kg/kW-hr
Indicated Specific Fuel consumption
𝑺𝑭𝑪 =
𝑰𝑷 (𝒊𝒏 𝒌𝒘)
× 𝟏𝟎𝟎
Brake Specific Fuel consumption
𝑺𝑭𝑪 =
× 𝟏𝟎𝟎
Piston speed = 2 L N, L = Stroke Length, N= Engine speed
Heat Balance Sheet
Heat supplied (𝐴) = 𝑸𝒔 = 𝒎𝒇 × 𝑪𝒗 𝐾𝐽/𝑚𝑖𝑛
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑸𝑩𝑷
𝑸𝑺
× 𝟏𝟎𝟎
𝑪𝑷𝑾 = 4.187 𝐾𝐽 /𝑘𝑔𝐾
𝑸𝑾
𝑸𝑺
× 𝟏𝟎𝟎
𝑤ℎ𝑒𝑟𝑒 𝑚𝑒𝑥ℎ = 𝑚𝑎 + 𝑚𝑓 ≈ [
𝑚𝑎
𝑚𝑓
] =
𝐴𝑖𝑟
𝐹𝑢𝑒𝑙
𝑪𝑷𝒈 = = 1.005 KJ/kgK
𝑸𝒈
𝑸𝑺
× 𝟏𝟎𝟎
𝑄𝑈𝑛𝑎𝑐𝑐𝑜𝑢𝑛𝑡 = 𝑄𝑠 − (𝑄𝐵𝑃 + 𝑄𝑊 + 𝑄𝑔) 𝐾𝐽 /𝑚𝑖𝑛
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝒔 = (𝑸𝑩𝑷 + 𝑸𝑾 + 𝑸𝒈 + 𝑸𝑼𝒏𝒂𝒄𝒄𝒐𝒖𝒏𝒕)
Morse test.
𝜼 (𝒎𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍) =
𝑰𝑷
× 𝟏𝟎𝟎

Previous Year Questions for 2a & 2b
Modal Question paper 1
Torque = T = (W-S) × R in N-m Effective
radius of the brake
R = (D+ d)/2
𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟𝑰𝑷
= 𝒏 𝑷𝒎 𝑳𝑨𝑵𝑲 (
𝟏𝟎
𝟔
)
K = 1 for 2S engine and ½ for 4S
engine
𝐵𝑟𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑟 𝑩. 𝑷
=
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Heat Balance Sheet
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑸𝑩𝑷
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑾
𝑸𝑺
× 𝟏𝟎𝟎
𝑚𝑎
𝑚𝑓
] =
𝐴𝑖𝑟
𝐹𝑢𝑒𝑙
𝑸𝒈
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑺
× 𝟏𝟎𝟎

Modal Question paper 2
Torque = T = (W-S) × R in N-m Effective
radius of the brake
R = (D+ d)/2
𝟏𝟎
𝟔
)
K = 1 for 2S engine and ½ for 4S
engine 𝐵𝑟𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑟 𝑩. 𝑷
=
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Indicated Thermal Efficiency 𝜼(𝒕𝒉) =
𝑰𝑷
𝒎𝒇×𝑪𝒗
× 𝟏𝟎𝟎
Heat Balance Sheet
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑸𝑩𝑷
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑾
𝑸𝑺
× 𝟏𝟎𝟎
𝑚𝑎
𝑚𝑓
] =
𝐴𝑖𝑟
𝐹𝑢𝑒𝑙
𝑸𝒈
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑺
× 𝟏𝟎𝟎

Jan 2019
Heat Balance Sheet
𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝒐𝒏 𝒎𝒊𝒏𝒖𝒕𝒆 𝒃𝒂𝒔𝒊𝒔: 𝑸𝑩𝑷
= 𝑩. 𝑷 × 𝟔𝟎 𝐾𝐽 /𝑚𝑖𝑛
𝑸𝑩𝑷
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑾
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝒈 = 𝒎𝒆𝒙𝒉 × 𝑪𝑷𝒈
× [𝑻𝑬𝒙𝒉 − 𝑻𝒓𝒐𝒐𝒎] 𝐾𝐽 /𝑚𝑖𝑛
𝑤ℎ𝑒𝑟𝑒 𝑚𝑒𝑥ℎ = 𝑚𝑎
+ 𝑚𝑓 ≈ [
𝑚𝑎
𝑚𝑓
] =
𝐴𝑖𝑟
𝐹𝑢𝑒𝑙
𝑸𝒈
𝑸𝑺
× 𝟏𝟎𝟎
𝑸𝑺
× 𝟏𝟎𝟎

July 2018
Torque = T = (W-S)×R in N-m
Brake Thermal Efficiency
𝜼(𝒕𝒉) =
𝑩𝑷
× 𝟏𝟎𝟎
𝑺𝑭𝑪 =
× 𝟏𝟎𝟎
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Indicated Thermal Efficiency
𝜼(𝒕𝒉) =
𝑰𝑷
× 𝟏𝟎𝟎
Morse test.
𝜼 (𝒎𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍) =
𝑰𝑷
× 𝟏𝟎𝟎

Jan 2020
Torque = T = (W-S) × R
in N-m Effective radius of
the brake
R = (D+ d)/2
Brake load or net load =
(W-S) in Newton
𝟏𝟎
𝟔
)
K = 1 for 2S engine and ½ for
4S engine
𝐵𝑟𝑎𝑘𝑒 𝑝𝑜𝑤𝑒𝑟 𝑩. 𝑷 =
𝟐𝝅𝑵𝑻
𝟔𝟎 × 𝟏𝟎𝟎𝟎
𝑩𝑷
𝑰𝑷
× 𝟏𝟎𝟎
Indicated Thermal Efficiency 𝜼(𝒕𝒉) =
𝑰𝑷
𝒎𝒇×𝑪𝒗
× 𝟏𝟎𝟎
Brake Thermal Efficiency 𝜼(𝒕𝒉) =
𝑩𝑷
𝒎𝒇×𝑪𝒗
× 𝟏𝟎𝟎
𝑺𝑭𝑪 =
× 𝟏𝟎𝟎

APPLIED THERMODYNAMICS 18ME42 Module 01 question no 2a &2b

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