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Brij Bhooshan Asst. Professor B.S.A College of Engg. & Technology, Mathura (India)

Copyright by Brij Bhooshan @ 2013

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Please welcome for any correction or misprint in the entire manuscript and your

valuable suggestions kindly mail us [email protected].

1. Determine the theoretical horse-power of an Otto cycle engine with a maximum

cycle temperature of 1395°C. The engine has a bore of 87.32 mm and a stroke of

108 mm. The clearance volume is 108.15 cm3. The engine operates of a 4-stroke

cycle at a speed of 3600 rpm. The pressure and temperature of the surrounding air

are 1 kg/cm2 and 4.5° C respectively. The engine has 6 cylinders and the volumetric

efficiency is 80%.

To increase the mass of air intake the above engine has been equipped with a

super changer that raises the inlet pressure to 122 cm of Hg (absolute). Determine

the new theoretical HP of the engine and the effective cycle efficiency. Assume Rair

= 29.7 kg m/kg K and Cv = 0.24.

2. A stoichiometric mixture of fuel and air has an enthalpy of combustion of

approximately-670 kcal/kg of mixture. In order to approximate an actual spark

ignition engine using such a mixture, consider an air-standard Otto cycle that has

a heat addition of 670 kcal/kg of air: a compression ratio of 8, and a pressure and

temperature at the beginning of compression process of 1.0 kgf/cm2 and 27°C.

Determine the maximum pressure and temperature in this cycle, the thermal

efficiency and the mean effective pressure. Assume CP = 0.24 and CV = 0.17.

3. An ideal gas internal combustion engine operates on a cycle which when

represented on a P-v diagram is a rectangle, P1 and P2 are the lower and higher




2 Problems of Practices on I. C. Engine

pressures respectively, v1 and v2 are the lower and higher volumes respectively.

Show that the thermal efficiency of the engine is

4. A six cylinder four stroke petrol engine has a swept volume of 300 cm3 per cylinder,

a compression ratio of 10, and operates at speed of 3500 rev/min. If the engine is

required to develop an output of 75 KW at this speed, calculate the cycle efficiency,

the necessary rate of heat addition, the mean effective pressure and the maximum

temperature of the cycle. Assume that the engine operates on the Otto cycle and

that the pressure and temperature before isentropic compression are 1 bar and 15 ⁰

C respectively. Take CP = 0.718; γ = 1.4.

5. If the above engine is a compression ignition engine operating on the Diesel cycle

and receiving heat at the same rate, calculate the efficiency, maximum

temperature of cycle, cycle efficiency, power output and the mean effective

pressure.

6. An experimental four stroke petrol engine of 1710 cm3 capacity is to develop

maximum power at 5400 rpm. The volumetric efficiency at this speed is assumed to

be 70 percent and the air-fuel ratio is 13 :1. Two carburetors are to be fitted and it

is expected that at peak power, the air speed at choke will be 107 m/sec. The

coefficient of discharge for the venturi is assumed to be 0.85 and that of the main

petrol jet 0.66. An allowance should be made for the emulsion tube, the diameter of

which can be taken as 1/2.5 of the choke diameter. The petrol surface is 6 mm

below the choke at this engine condition. Calculate the sizes of suitable choke and

main jet. The specific gravity of petrol is 0.75 Atmospheric pressure and

temperature are 1.013 bar and 27⁰ C respectively.

7. A single-cylinder 4-stroke gas engine with a hit and miss governing has 200 mm

bore and 400 mm stroke. It recorded a gas consumption of 153 liter/min at 8.75 cm

of water above atmospheric pressure, when barometer reading was 759 mm of

mercury, atmospheric and gas temperature was 17 °C. The gas used had gross

calorific value of 18200 kJ/m3 and density 0.592 kg/m3 both at N.T.P. hydrogen

present in the gas was 12 per cent by mass, air consumed was 0.0242 kg/s, for dry

exhaust gas was 1.05 kJ/kg K. The mean effective pressure of positive loop was

5.72 and of negative loop 0.274 bar in firing and 0.38 bar in missing strokes, the

engine speed as 285 rpm; and explosions per minute 114. The brake torque was

330 Nm. Cooling water used was 9.2 kg per minute with its temperature raised by

20° C. Exhaust temperature was 400 ⁰C. The total heat of steam at atmospheric

pressure is 2676 kJ per kg and Cp for superheated steam 1.8 kJ/Kg K.

Calculate the percentage of the indicated power used for pumping work and for

mechanical friction and draw up an energy balance for the engine.

8. An eight cylinder petrol engine is to deliver 160 b.h.p. at a piston speed 750 m per

minute with an indicated thermal efficiency of 23 percent. The stroke to bore ratio

is 1.25 the volumetric efficiency is 85 percent (1.0 kg/cm2 and 40° C intake

condition) and mechanical efficiency is 83 percent. Assume petrol contains 10,200

kcal of heat kcal of heat of combustion per kg and requires 14 kg of air per kg for

complete combustion. The engine uses a mixture having 10 per cent excess air.

Calculate the diameter of the cylinder and stroke, the brake specific fuel

consumption and the brake mean effective pressure.




3 Problems of Practices on I. C. Engine By Brij Bhooshan

9. What is the percentage change in the efficiency of Otto cycle having a compression

ratio 7, if the specific heat at constant volume increases by 1%?

10. A two stroke engine subjected to full load test gave the following results:

Cylinder dia 22 cm

Stroke 27 cm

Brake dia 1.5 m

Speed 450 rev/min

brake load 4.6 kg

imep 2.9 kgf/cm2

fuel consumption 5.4 kg/hr

rise in temperature of jacket water 36º C

jacket water flow 440 kg/hr

air/fuel ratio by mass 31

temperature of exhaust gas 355ºC

room temperature 20º C

atmospheric pressure 76 cm Hg

calorific value of fuel 10500 kcal/kg

proportion of hydrogen by mass in fuel 15

Take R = 29.27 for air CP = 0.24 for exhaust gas CP = 0.49 kcal/kg K for dry steam.

Determine:

(i) the indicated thermal efficiency

(ii) the specific fuel consumption in gm/BHP hr

(iii) the volumetric efficiency

(iv) Draw up the heat balance on percentage basis.

11. A four cylinder two stroke cycle diesel engine running at 3000 rpm has a bore of

120 mm and stroke of 125 mm. The brake torque was measured as 420 Nm. The

volumetric efficiency of the engine is 0.62. The air fuel ratio is 21 : 1. Calorific

value of the fuel is 45000 kJ/kg. The density of air at suction was 1.1 kg/m3.

Determine the brake thermal efficiency and brake mean effective pressure. If an

orifice tank with orifice diameter of 90 mm was used, determine the water head

across the orifice. Take coefficient of discharge for orifice (Cd) =0.60.

12. A single cylinder, two-stroke oil engine gave the following lest data:

Cylinder bore = 150 mm, stroke = 250 mm, engine speed 420 rev/min, the brake

consists of a belt carrying a dead load of 48 kg on one end while the other end is

attached to a sprig balance reading 3 kg, the mean diameter of the friction brake =

1 m, area of indicator diagram = 2.8 cm2, length of indicator diagram = 6.75 cm, the

indicator spring rating is 0.92 mm/bar.

Calculate the mechanical efficiency of the engine.

13. The mass analysis of the petrol used in an engine was 85% C and 15% H2. The dry

exhaust gas analysis showed that the parentage by volume of carbon dioxide was

six times that of oxygen and that no carbon-monoxide was present Calculate:

(i) The air-fuel ratio by mass,

(ii) The percentage excess air supplied

Assume air contains 23.2% O2 by mass or 20.9% O2 by volume.

14. The following data related to a test trial of a single -cylinder four-stroke gas

engine:

(i) Cylinder dia. 24 cm. stroke length 48 cm.





(ii) Compression ratio = 5.9

(iii) Net brake load applied at brake wheel having an effective circumference of

3.86 m is 1260 N at average speed of 227r.p.m.

(iv) Number of explosions/minute = 77.

(v) Gas used/mt at 771 mm of mercury and 15°C = 0.217

(vi) Lower calorific value of gas at NTP = 49350 kJ/m3.

(vii) Mean effective pressure from indicator card = 7.5 bar

(viii) Weight of Jacket cooling water/mt = 11 kg

(ix) Temperature rise of cooling water = 34.2 °C

(x) Specific heat of water = 4.2 kJ/kg °C

Estimate (i) mechanical efficiency, (ii) indicated thermal efficiency and (iii)

efficiency ratio, and draw a heat balance sheet for the engine assuming that

exhaust gases carry away 24% of heat.

15. A four cylinder engine of a truck has been converted to run on propane fuel. A dry

analysis of the engine exhaust gives the following volumetric percentages:

CO2 = 4.90; CO = 9.79 and O2 = 2.45.

Calculate the equivalence ratio at which the engine is operating.

16. A three liter V 6 S.I. engine operates on a four stroke cycle at 3600 rpm. The

compression ratio is 9.5, the length of the connecting rod is 16.6 cm and the engine

is square (bore = stroke). At this speed, the combustion ends at 20°ATDC.

Calculate:

(i) cylinder bore and stroke length

(ii) average piston speed

(iii) clearance volume of one cylinder

(iv) piston speed at the end of combustion

(v) Distance the piston has travelled from TDC at the end of combustion.

(vi) Volume in the combustion chamber at the end of combustion.

17. Derive an expression for the air-fuel ratio delivered by a simple carburetor. Discuss

its limitations. What are the systems incorporated to overcome the limitations of a

simple carburetor?

18. The exhaust gas analysis of an engine using Octane (C8H18) as fuel gives equal

volumes of CO2 and unused O2. Compute the actual and stoichiometric air-fuel

ratios. For equivalence ratio of 1, calculate:

(i) the volume of mixture per kg of fuel at pressure of 100 kPa and

temperature 70 °C

(ii) The volume of the products of combustion per kg of fuel when the

temperature of products of combustion is 127 °C at pressure 1 bar.

19. A 4-stroke petrol engine of 2 liters capacity is to develop maximum power at 4000

rpm. The volumetric efficiency at this speed is 0.75 and the air-fuel ratio is 14 : 1.

The venturi throat diameter is 28 mm. The coefficient of discharge of venturi is

0.85 and that for fuel jet is 0.65. Calculate:

(i) the air velocity at the throat and

(ii) The diameter of the fuel jet.

The specific gravity of petrol is 0.76. Atmospheric pressure and temperature are 1

bar and 17°C respectively.

20. The brake thermal efficiency of a diesel engine is 30%. If the air to fuel ratio by

weight is 20 and the calorific value of fuel is 41800 kJ/kg, find brake mean effective

pressure at S.T.P. (15°C and 760 mm of Hg).





21. A six cylinder, four stroke petrol engine with a bore of 120 mm and stroke of 180

mm under test, is supplied petrol of composition: C = 82% and H2 = 18% by mass.

The Orsat gas analysis indicated that CO2 = 12%, O2 = 4% and N2 = 84% by

volume. Determine (i) that air-fuel ratio and (ii) the percentage of excess air.

Also calculate the volumetric efficiency of engine based on intake conditions when

the mass flow rate of petrol 32 kg/min at 1600 RPM. Intake conditions are 1 bar

and 17°C. Consider the density of petrol vapour to be 3.5 times that of air at same

temperature and pressure. Air contains 23% oxygen by mass.

22. The venturi of a sample carburetor has a throat diameter of 20 mm and the fuel

orifice has a diameter of 1.12 mm. The level of petrol surface in the float chamber

is 6.0 mm below the throat venturi. Coefficient of discharge for venturi and fuel

orifice are 0.85 and 0.78 respectively. Specific gravity of petrol is 0.75. Calculate (i)

the air-fuel ratio for a pressure drop of 0.08 bar, (ii) petrol consumption in kg/hr

and (iii) the critical air velocity. The intake conditions are 1.0 bar and 17°C. For air

Cp = 1.005 and Cv = 0.718 kJ/kg-K.

23. An eight cylinder automobile engine of 80 mm diameter and 90 mm stroke with a

compression ratio of 7, is tested at 4000 RPM on a dynamometer of 600 mm arm

length. During a ten minutes test period at a dynamometer scale reading of 450 N,

4.8 kg of gasoline having a calorific value of 45000 kJ/kg was burnt and air at 27°C

and 1.0 bar was supplied to the carburetor at the rate of 6.6 kg/min. Find (i) the

brake power delivered, (ii) the brake mean effective pressure, (iii) the brake specific

fuel consumption, (iv) brake thermal efficiency, (v) the volumetric efficiency and

(vi) the air-fuel ratio.

24. Determine the air-fuel ratio at 6000 m altitude in a carburetor adjusted to give an

air-fuel ratio of 15 : 1 at sea level where air temperature is 27° C and pressure is

1.013 bar. The temperature of air decreases with altitude and is given by the

expression

where h is height in meters and ts is the sea level temperature in °C.

The air pressure decreases with altitude as per the relation

where P is in bar.

25. The air flow to a four cylinder 4-stroke oil engine is measured by means of a 4.5 cm

diameter orifice, having Cd = 0.65. During a test the following data was recorded:

Bore =1.0 cm,

Stroke =1.5 cm,

Engine speed = 1000 RPM,

Brake torque = 135 Nm,

Fuel consumption = 5.0 kg/hour,

CVfuel = 42600 kJ/kg,

Head across orifice = 6 cm of water,

Ambient temperature and pressure are 300 K and 1.0 bar respectively.

Calculate:

(i) Brake thermal efficiency

(ii) The brake mean effective pressure

(iii) The volumetric efficiency

Take R = 287 J/kg K for air.





26. An 8-cylinder, 4-stroke diesel engine has a power output of 368 kW at 800 RPM.

The fuel consumption is 0.238 kg/kW-hr. The pressure in the cylinder at the

beginning of injection is 35 bar and the maximum cylinder pressure is 60 bar. The

injector is adjusted to operate at 210 bar and the maximum pressure in the injector

is set at 600 bar. Calculate the orifice are a required per injector if the injection

takes place over 12°crank angle. Assume the coefficient of discharge for the injector

= 0.6, specific gravity of fuel = 0.85 and the atmospheric pressure = 1.013 bar. Take

the effective pressure difference to be the average pressure difference over the

injection period.

27. An I.C. engine fuel has the following composition:

C = 89%, H2 = 5%, O2 = 4% and rest N2.

Determine the chemically correct air-fuel ratio. If 40% excess air is supplied, find

the percentage of dry products of combustion by volume.

28. A six-cylinder, 4-stroke petrol engine has a swept volume of 3.0 liters with a

compression ratio of 9.5. Brake output torque is 205 N-m at 3600 r.p.m. Air enters

at 85 N/m2 and 60° C. The mechanical efficiency of the engine is 85% and air-fuel

ratio is 15 : 1. The heating value of fuel is 44,000 kJ/kg and the combustion

efficiency is 97%. Calculate:

(i) Rate of fuel flow

(ii) Brake thermal efficiency

(iii) Indicated thermal efficiency

(iv) Volumetric efficiency

(v) Brake specific fuel consumption

29. A 4-stroke petrol engine has a swept volume of 20 liters and is running at 4000

r.p.m. The volumetric efficiency at this speed is 0.75 and the air-fuel ratio is 14 :1.

The venturi throat diameter of the carburettor fitted to the engine is 30 mm.

Estimate the air velocity at the throat if the discharge coefficient for air is 0.9.The

ambient conditions are: pressure = 1.0 bar, temperature = 20° C. Calculate the

diameter of the fuel jet if the fuel density is 760 kg/m3.

For air Cp = 1.005 kj/kg K and R = 287 J/kg K. Assume Cdf = 1.0.

30. Derive an expression for air-fuel ratio delivered by a simple carburetor, neglecting

the effect of compressibility. Discuss the limitations of simple carburetor. What are

the modifications incorporated for its use in automotive vehicles?

31. A four-stroke petrol engine develops 30 kW at 2600 r.p.m. The compression ratio of

the engine is 8 and its fuel consumption is 8.4 kg/h with calorific value of 44 MJ/kg.

The air consumption of the engine as measured by means of a sharp edge orifice is

2 m3 per min. If the piston displacement volume is 2 liters, calculate:

(i) Volumetric efficiency

(ii) Air-fuel ratio

(iii) Brake mean effective pressure

(iv) Brake thermal efficiency

(v) Relative efficiency

The ambient temperature of air can be taken as 27 °C, R for air as 287 J/kg-K and

γ = 1.4. The barometer reads 755 mm of mercury.

32. A simple carburetor has a venturi throat diameter of 20 mm and the coefficient of

flow is 0.8. The diameter of the fuel orifice is 1.14 mm and the coefficient of fuel is

0.65. The gasoline surface is 5 mm below the throat. Calculate-

(i) the air-fuel ratio for a pressure drop of 0.08 bar when the nozzle tip is





neglected;

(ii) the air-fuel ratio when the nozzle tip is taken into account;

(iii) the minimum velocity of air or critical air velocity required to start the fuel

flow when the nozzle tip is provided.

Assume the density of air and fuel to be 1.20 kg/m3 and 750 kg/m3 respectively,

33. The following set of observations refer to a trial on a Single-cylinder, Four-stroke,

Solid injection diesel engine of 200 mm-bore and 400 mm stroke:

Gross mean effective pressure = 6.2 bar

Pumping mean effective pressure = 0.44 bar

Speed of the engine = 262 rpm

Brake torque = 668 N-m

Fuel supply rate = 4.5 kg/hr

Calorific value of the fuel = 52,000 kJ/kg

Cooling water flow rate = 6 kg/min

Cooling water temperature gain = 47°C

Calculate the Indicated Power, Brake Power and Mechanical efficiency of the

engine.

Draw up a heat balance sheet for the trial expressing various quantities in kJ/min,

if the fuel contains 13.5% H2 (by mass) and air supply to the engine is 2.71 kg/min

at 17°C. The exhaust gases leave the engine at 400°C. The following data may be

used:

Mean specific heat of exhaust gases = 1 kJ/kgK

Specific heat of steam = 2.1 kJ/kgK

Latent heat of steam = 2250 kJ/kg

Estimate the heat carried away by steam in exhaust gases.

34.

During a test on a two stroke engine on full load, the following observations were

recorded:

Speed = 350 rpm

Net brake load = 590 N

Mean effective pressure = 2.8 bar

Fuel oil consumption = 4.3 kg/h

Cooling water required = 500 kg/h

Rise in cooling water temperature = 25°C

Air used per kg of fuel = 33 kg

Room temperature = 25°C

Exhaust gas temperature = 400°C

Cylinder diameter = 220 mm

Stroke length = 280 mm

Effective brake diameter = 1 m

C.V. of fuel oil = 43900 kJ/kg

Proportion of hydrogen in fuel = 15%

Mean specific heat of exhaust gases =1.0 kJ/kg-K

Specific heat of steam = 2.09 kJ/kg-K

Calculate the following:

(i) Indicated power

(ii) Brake power

(iii) Draw heat balance sheet on the basis of kJ/min.

35. Two identical petrol engines having the following specifications are used in





vehicles:

Engine 1: Swept volume = 3300 cc, Normally aspirated, bmep = 9.3 bar, rpm

= 4500, Compression ratio = 8.2, Efficiency ratio = 0.5, Mechanical

efficiency = 0.9, Mass of the engine = 200 kg.

Engine 2: Super charged, Swept volume = 3300 cc, bmep = 12.0 bar, rpm =

4500, Compression ratio = 5.5, Efficiency ratio = 0.5, Mechanical

efficiency = 0.92, Engine mass = 220 kg.

If both the engines are supplied with just adequate quantity of petrol for the test

run, determine the duration of test run so that the specific mass per kW of brake

power is same for both the engines. Calorific value of petrol = 44000 kJ/kg,

Assume both the engines operate on four stroke cycle.

Also compare two engines and suggest their applications with reasoning.

36. An energy using 10 moles of diatomic ideal gas works on the reversible cycle

having the following processes:

(i) Adiabatic compression from 1 bar pressure and 300 K temperature to

pressure of 9 times the initial value,

(ii) Constant pressure transformation upto temperature of 1000 K,

(iii) Adiabatic expansion upto 3 bars,

(iv) Constant pressure transformation such that temperature of 1000 K is

reached,

(v) Adiabatic expansion,

(vi) Constant pressure transformation upto the original state.

For this engine,

(a) Represent the cycle on a p-v diagram.

(b) Calculate pressure, temperature and volume at salient points.

(c) Calculate the efficiency of the engine summarizing results in a tabular form.

Compare the efficiency of the engine operating on Carnot cycle between the same

extreme temperatures. Give comments.

37. A taxicab is equipped with a flexible four cylinder S.I. engine running on a mixture

of methanol and gasoline at an equivalence ratio of 0.95. How must the air-fuel

ratio change as the fuel flow to the engine shifts from 10% methanol (M10) to 85%

methanol (M85)?

38. During a trial of a single cylinder, 4 stroke diesel engine the following observations

were recorded:

Bore = 340 mm

Stroke = 440 mm

rpm = 400

Area of indicator diagram = 465 mm2

Length of diagram = 60 mm

Spring constant = 0.6 bar/mm

Load on hydraulic dynamometer = 950 N

Dynamometer constant = 7460

Fuel used = 10.6 kg/h

Calorific value of fuel (C) = 49500 kJ/kg

Cooling water circulated = 25 kg/min

Rise in temp, of cooling water =25°C

Mass analysis of fuel:

Carbon = 84%





Hydrogen =15%

Incombustible =1%

Volume analysis of exhaust gas:

Carbon dioxide = 9 %

Oxygen =10%

Temp, of Exhaust gases = 400°C

Sp. heat of exhaust gas =1.05kJ/kg°C

Partial pressure of steam in exhaust gas = 0.030 bar

Sp. heat of superheated steam =2.1kJ/kg °C

Saturation temp, of steam at 0.030 bar = 24.1°C

Draw up heat balance sheet on minute basis.

39. What is meant by firing order in internal combustion engines?

What are the firing orders used in 4 and 6 cylinder inline engines?

What are the three purposes of firing order in V engines?

40. In a 4-stroke, 2-cylinder diesel engine, the following data was collected:

Piston stroke = 60 cm

Diameter of the cylinder = 40 cm

Speed of the engine = 250 r.p.m.

Indicated mean effective pressure = 8 bar

Brake power of the engine = 220 kW

Fuel consumption = 80 kg/hr

CV of fuel used = 43000 kJ/kg

Hydrogen content in fuel = 13% and remaining is carbon

Air consumption = 30 kg/min

Cooling water circulated = 90 kg/min

Rise in temperature of cooling water = 38 °C

Piston cooling oil used = 45 kg/min

Rise in temperature of cooling oil = 23 °C

Cp of water = 4.18 kJ/kg-K

Cp of cooling oil = 2.2 kJ/kg-K

Cp of exhaust gases = 1.1 kJ/kg-K

Cp of superheated steam = 2 kJ/kg-K

Latent heat of steam = 2520 kJ/kg

Exhaust gas temperature = 450 °C

Ambient temperature = 27 °C

Find the following quantities per minute:

(i) Heat converted to useful brake power (BP)

(ii) Heat carried away by cooling water

(iii) Heat carried away by cooling oil

(iv) Heat carried away by dry exhaust gases

(v) Heat carried away by steam formed

(vi) Heat supplied by fuel

Draw up also a heat balance sheet on minute basis and percentage basis.

41. A 2-stroke oil engine was subjected to a test at room temperature of 20 °C with fuel

oil of calorific value 44000 kJ/kg. Calculate the indicated and brake, power,

mechanical and brake thermal efficiency, and draw the heat balance sheet using

the following data:

Cylinder bore = 20 cm; Stroke-bore ratio = 1.3 : 1; Speed = 500 r.p.m.; Brake drum





diameter = 120 cm; Rope diameter = 3 cm; Net brake load = 460 N; Indicated MEP

= 2.8 bar; Oil consumption = 3.7 kg/hr; Jacket cooling water rate = 456 kg/hr with a

rise in temperature of 27 °C; Exhaust gas temperature entering calorimeter is 320

°C and leaving 220 °C; Temperature rise in calorimeter water is 8 °C with a rate of

flow 8 kg/min

42. The following data refer to a 4-stroke, 4-cylinder diesel engine:

Cylinder diameter = 36 cm; Stroke = 40 cm; Speed = 315 r.p.m.; Indicated MEP = 7

bar; Brake power = 250 kW; Fuel consumption = 80 kg/hr; Calorific value = 44

MJ/kg; Air consumption = 30 kg/min; Cooling water circulated = 90 kg/min with

rise in temperature 38 °C; Exhaust gas temperature = 324 °C and Room

temperature = 45 °C kJ/kg K; Cpair = 1.005 kJ/kgK, Cpgas = 1.05 kJ/kg K, CPsteam =

2.093 kJ/kg K. In exhaust gases, partial pressure of steam is 0.03 bar and fuel

contains 13% H2.

Find mechanical efficiency, indicated thermal η, brake specific fuel consumption:

Draw heat balance sheet for the engine in hourly basis.

43. A nine (9)-cylinder, 4-stroke petrol engine of bore 14.5 cm and stroke 18 cm, has a

compression ratio of 7:1 and develops 350 kW at 2000 rpm when running on a

mixture of 15% weak. The fuel used has a heating value of 47 MJ/kg and contains

85.2% C and 14.8 H2. Assuming a volumetric efficiency of 76% at 15°C and 1 bar

and mechanical efficiency of 90%, calculate the indicated thermal efficiency of the

engine. Given, R = 287 J/kg-K.

44. A 2-stroke motor cycle petrol engine cylinder consists of 15 fins on its outer surface.

If the outside and inside diameters of each fin are 200 mm and 100 mm

respectively, the average fin surface temperature is 475°C and the atmospheric air

temperature is 25°C, calculate the heat transfer rate from the fins for the following

cases:

(i) the motor cycle is stationary;

(ii) when the motor cycle is running at a speed of 60 kmph.

The fin may be idealized as a single horizontal plate of the same area, and the

significant length may be taken as L = 0.9 d0, where d0 is the outer diameter of the

fin. Assume d0 as 200 mm.

The properties of air may be taken as follows:

k = 4.266 × l0−2 W/m°C; ν = 40.61 × l0−6 m2/s; Pr = 0.677

For turbulent flow (forced convection) : Nu = 0.036 (Re)0.8 (Pr)0.33

For natural convection :

Nu = 0.54. (Gr. Pr)1/4 if (Gr. Pr) < 109

Nu = 0.10 (Gr. Pr)0.33 if (Gr. Pr) > 109.

45. Determine the diameter of a fuel orifice for a 4-stroke engine working on diesel

cycle developing 18 kW per cylinder at 2000 revolutions per minute, using 0.27

kg/kW-hr fuel of 30° API. The duration of the crank injection is 30° of crank travel.

The fuel injection pressure is 125 bar and the combustion chamber pressure is 35

bar. Take velocity coefficient as 0.9 and

APIP

5.131

5.141

46. Determine, the air-fuel ratio at 6000 m altitude in a carburetor adjusted to give an

air-fuel ratio of 15 : 1 at sea level where the air temperature is 300 K and pressure

of 1.013 bar.





The temperature of air decreases with altitude and is given by the expression

t = ts 0.0065h

where h is altitude in meters and ts is the temperature at sea level in °C.

The air pressure decreases with altitude as per the relation

h = 19220 log10(1.013/P)

where, p is in bar.

What remedies would you suggest to compensate for the decrease in air fuel ratio

at high altitudes? Discuss them giving justification.

47. The following observations were made during a 30-minute trial of a single-cylinder,

four- stroke gas engine having cylinder diameter of 18 cm and stroke 24 cm,

running at 300 rpm.

Indicated mean effective pressure = 5, bar,

Total number of explosions = 4425,

Total gas consumption = 2.4 m3,

Calorific value of gas = 19000 kJ/m3,

Density of gas = 1.275 kg/m3,

Air consumption = 32.1 m3.

Density of air = 1.29 kg/m3,

Temperature of exhaust gases = 350° C,

Specific heat of gases = 1.0 kJ/kg-K,

Mass of cooling water circulated = 120 kg;

Rise in temperature of cooling water = 30°C.

Net load on the brake drum is 38 kg and the effective diameter of the brake

drum is 1 m.

Assuming room temperature of 27° C, calculate

(i) Indicated power,

(ii) Brake power,

(iii) Indicated thermal efficiency,

(iv) Mechanical efficiency, and

(v) Brake thermal efficiency.

Also draw up a heat balance sheet on per minute basis as well as percentage basis.

48. The venturi of a simple carburetor has a throat diameter of 20 mm and the fuel

orifice has a diameter of 1.12 mm. The petrol surface in the float chamber is 6 mm

below the throat of venturi. Coefficient of discharge for venturi and fuel orifice are

0.85 and 0.78 respectively. Density of petrol is 750 kg/m3. Calculate

(i) the air-fuel ratio for a pressure drop of 0.08 bar

(ii) the minimum air velocity at which petrol starts flowing into venturi

throat, and

(iii) petrol consumption in kg/hr.

Intake air condition is 1 bar and 17°C. For air take CP = 1.005 kJ/kg-K and Cv =

0.718 kJ/kg-K.

49. A 10 cm dia × 12 cm stroke, 4-cylinder. 4-stroke engine running at 2600 RPM has a

carburetor venturi of 3.2 cm throat. Determine the suction pressure at the throat

assuming the volumetric efficiency of the engine to be 70%. Assume density of air

to be 1.2 kg/m3 and coefficient of airflow 0.82. Neglect compressibility of air.

50. A diesel engine has a diameter of 20 cm and stroke of 30 cm. The clearance volume

is 10 percent of the swept volume. Estimate the compression ratio and the air-





standard efficiency of the engine if the cut-off takes place at 10 percent of the

stroke.

51. During the trial of a single-cylinder. 4-stroke oil engine, the following observations

were made:

Cylinder diameter = 20 cm;

stroke; = 45 cm;

mean effective pressure = 6 bars;

torque = 500 N-m;

speed = 260 RPM;

oil consumption = 4.5 kg/hr;

calorific value of fuel = 44000 kJ/kg;

cooling water flow rate = 5 kg/min;

air used/kg of fuel = 30 kg;

rise in cooling water temperature = 40 °C;

temperature of exhaust gases = 400 °C;

room temperature = 25 °C;

mean specific heat exhaust gases = 1.0 kJ/kg-K;

Specific heat of water = 4.18 kJ/kg-K.

Determine i.p., b.p., and draw a heat balance sheet for the test in kJ/hour.

52. The following data pertain to the testing of a four-cylinder, four-stroke diesel

engine:

Bore = 40 cm, Stroke = 44 cm, Speed = 400 r.p.m., bp = 380 kW, mep = 7.5 bar,

Fuel consumption = 85 kg/hr, Lower calorific value of fuel = 44 MJ / kg, Air

consumption = 35 kg/min, Mass of jacket water = 98 kg/min, Rise in temperature of

jacket cooling water = 40°C, Amount of piston cooling oil = 54 kg/min, Temperature

rise of cooling oil = 24 °C, Specific heat of cooling oil = 2.09 kJ/kg-K, Room

temperature = 20 °C, Exhaust gas temperature = 320 °C, Cp of dry exhaust gas =

1.045 kJ/kg-K.

Draw up the heat balance and calculate mechanical efficiency and brake specific

consumption at half-load if friction power remains the same. Comment on the

results in the light of modern diesel engines.

53. A four-cylinder, four-stroke square engine running at 40 rev/sec is with a

carburettor which is required to supply 5 kg of air and 0.5 kg of fuel per minute.

The fuel specific gravity is 0.75. The air is initially at 1 bar and 300 K. Calculate

the throat diameter of the choke for a flow velocity of 100 m/sec. Velocity coefficient

is 0.8. If the pressure drop across the fuel metering orifice is 0.80 of that of choke,

calculate the orifice diameter assuming Cdf = 0.60 and γ = 1.4. If the carburettor

venturi has a 3 cm throat, assuming the bore to be 10 cm, volumetric efficiency of

75%, the density of air to be 1.15 and coefficient of airflow to be 0.75 , calculate the

suction at the throat.

54. A four-cylinder, four-stroke diesel engine develops a power of 180 kW at 1500

r.p.m. The brake specific fuel consumption (bsfc) is 0.2 kg/kWh. At the beginning of

injection, pressure is 30 bar and the maximum cylinder pressure is 50 bar. The

injection is expected to be at 200 bar and maximum pressure at the injector is set

to be about 500 bar. Assume the following:

Cd for injector = 0.7

SG of fuel = 0.875

Atmospheric pressure = 1 bar





Effective pressure difference = Average pressure difference over the

injection period.

Determine the total orifice area required per injector if the injection takes place

over 15° crank angles.

55. A four-stroke cycle gas engine has a bore of 20 cm and a stroke of 40 cm. The

compression ratio is 6. In the test on the engine the indicated mean effective

pressure is 5 bar, the air to gas ratio is 6 : 1 and the calorific value of the gas is 12

MJ/m3 at NTP. At the beginning of the compression stroke, the temperature is

77°C and pressure 0.98 bar. Neglecting residual gases, determine the indicated

power, the thermal efficiency and the relative efficiency of the engine at 250 r.p.m.

56. The pressure on the compression curve of a diesel engine are, at l/8th stroke 1.4 bar

and at 7/8th stroke 14 bar. Estimate the compression ratio. Calculate the air

standard efficiency of the engine if the cut-off occurs at l/15th of the stroke. Also

find the fuel consumption per kWhr if the indicated thermal efficiency is 0.5 of

ideal efficiency, mechanical efficiency is 0.8 and the calorific value of the fuel is

41,900 kJ/kg. Take γ = 141.

57. An automobile has a 3.2 liter, five cylinder, four stroke cycle diesel engine

operating at 2400 RPM. Fuel injection occurs from 20° b TDC to 5° a TDC. The

engine has a volumetric efficiency of 0.95 and operates with fuel equivalence ratio

of 0.80. Light diesel fuel is used.

Calculate: (i) time for one injection, (ii) fuel flow rate through an injector.

Take stoichiometric air-fuel ratio as 14.5.

58. Prove that for the same compression ratio the Otto is more efficient than Diesel

cycle.

59. In a simple carburetor, the petrol in the float chamber stands 6 mm below the jet

opening. The engine consumes 6.4 kg fuel/h. The fuel jet diameter is 1.25 mm and

the discharge coefficient of the fuel orifice is 0.64. If the air-fuel ratio is 16 : 1,

estimate –

(i) the air velocity at the throat;

(ii) the throat diameter;

(iii) the pressure drop in cm of water.

The coefficient of discharge for air is 0.85 and the ambient conditions are pressure

= 1 bar and temperature = 288 K. Take the density of fuel and air as 770 kg/m3 and

1.1122 kg/m3 respectively. Neglect compressibility effect.

60. The following data relates to a two-cylinder four-stroke coal gas engine:

Bore and stroke of cylinder = 380 mm and 585 mm respectively

At 240 rpm, torque developed = 5.16 kNm

Coal gas to air mixture ratio = 1 to 7 by volume

Estimated volumetric efficiency = 85%

Net calorific value of coal gas = 16800 kJ/kg

Calculate the brake power, brake mean effective pressure, piston speed in meter

per second and brake thermal efficiency.

61. The cylinder volume of an I.C. engine is 3000 cm3. It contains products of

combustion in gaseous form, which can be assumed to be an ideal gas. The

combustion products, just before the exhaust valve opens, are at a pressure of 6 bar

and temperature of 1123 K. Assuming specific heats at constant volume and

constant pressure as 0.718 and 1.005 kJ/kg-K respectively, analyse and discuss the

availability of specific energy of the gas. The initial pressure and temperature of





gas can be taken as 1 bar and 15°C respectively.

62. A petrol engine with a compression ratio of 7 uses a mixture of isooctane and

hexane as fuel. The pressure and temperature at the beginning of the compression

process are 1 bar and 55.22 °C respectively. If the fuel-air mixture is 19.05% rich

and the maximum pressure developed is 115.26 bar, evaluate the composition of

the mixture (in percentage weight).

Take, Cv = 0.717 kJ/kg-K, (CV)hexane = 43 MJ/kg, (CV)isooctane = 42 MJ/kg and PV1.31 is

constant for the expansion and compression processes.

63 Petrol used in SI engine is assumed to have a chemical formula C7H16; Determine:

(i) stoichiometric A/F ratio.

(ii) If 50% excess air is supplied then find the volumetric composition of dry

exhaust products.

Air contains 23% of O2 & 77% of N2 by Mass.

64. A test on a single cylinder engine, four stroke having bore 180 mm and stroke 360

mm yielded the following results:

Speed : 285 rev/min.

Brake Torque : 393 Nm

IMEP : 7.2 bar

Fuel consumption : 3.5 kg/hr

Cooling water flow : 4.5 kg/ min

Cooling water temp, rise : 36º C

A/F ratio by mass : 25

Exhaust gas temp. : 415º C

Barometric pressure : 1.013 bar

Room temperature : 21º C

Fuel has a calorific value 45200 kj/kg and contains 15% by mass of hydrogen.

Determine:

(i) indicated thermal efficiency.

(ii) The volumetric efficiency based on atmospheric conditions.

(iii) Draw up a heat balance in terms of kJ/min explaining clearly the

content of such term.

Take R = 0.287 kJ/kgK,

CV for dry exhaust gases = 1.005 kJ/kgK

Cp for superheated steam = 2.05 kJ/kgK.

65. A 4 stroke single cylinder diesel engine develops a 36 kW when running at 800

rpm and consumes 240 gms/kWh. The pressure of the air in the cylinder at the

beginning of injection and at the end of injection are 40 bar and 60 bar. The

injection pressure at the beginning and end of injection are 200 bar and 600 bar

respectively.

Determine the diameter of the nozzle if the injection is carried out during 15°

rotation of the crank. The ambient pressure and temp, are 1.013 bar and 27°C. Cdf

= 0.6 and ρf = 800 kg/m3.

66. An automobile has 3.2 liter five cylinder, four stroke cycle diesel engine operating

at 2400 rpm. Fuel injection occurs from 20° b TDC to 5° a TDC. The engine has a

volumetric efficiency of 0.95 & operates with fuel equivalence ratio of 0.80. Light

diesel fuel is used. The pressure is 101 kPa, Temp. 298 K, R = 0.287 kJ/kg K.

Calculate





(i) Time for one injection.

(ii) Fuel f1ow rate through an-injector.

67. Derive an expression for air standard efficiency of dual combustion cycle in terms

of compression ratio, cut-off ratio, and ratio of specific heats.

68. The compression ratio of an air standard Otto cycle is 8. At the beginning of

compression process the pressure is 1 bar and temperature 300 K. The heat

transfer to the air per cycle is 1900 kJ/kg of air. Calculate thermal efficiency and

mean effective pressure.

69. The following data is given for a 4 stroke, 4 cylinder diesel engine:

Diameter of cylinder = 35 cm, Piston stroke = 40 cm, Speed = 315 rpm, Imep = 7

bar, BP = 260 kW, TFC = 80 kg/hr, CV of fuel used = 43000 kJ/kg, Hydrogen

content of fuel = 13% and remaining is carbon. Air consumption 30 kg/min,

cooling water circulated 90 kg/min, Rise in temperature of cooling water 38°C,

piston cooling oil used 45 kg/min. Rise in temperature of cooling oil 23°C, for

cooling oil Cp = 2.3 kJ/kgK, exhaust gas temperature 322°C and Cp for exhaust

gas 1.1 kJ/kgK, Ambient temperature 22°C, Cp for superheated steam 2 kJ/kgK

and latent heat of steam 2520 kJ/kg. Find: (i) Mechanical and indicated thermal

efficiency, and (ii) Draw up the heat balance sheet on minute basis.

70. A two-stroke CI engine delivers a brake power of 368 kW, while 73.6 kW is used to

overcome friction losses. It consumes 180 kg/hr of fuel at an air-fuel ratio of 20:1.

The heating value of the fuel is 42000 kJ/kg. Calculate (i) indicated power, (ii)

mechanical efficiency, (iii) air consumption, (iv) indicated thermal efficiency and (v)

brake thermal efficiency.

71. A six-cylinder petrol engine develops 62 hp at 3000 RPM. The volumetric efficiency at

NTP is 85%. The bore is equal to the stroke and thermal efficiency of 25% may be

assumed. Calorific value of petrol is 10500 kcal/kg. Air-fuel ratio is to be 15:1.

Calculate cylinder bore and stroke.

72. A four-cylinder four-stroke petrol engine was subjected to a laboratory test and the

following data were obtained:

Cylinder diameter = 64 mm

Stroke length - 90 mm

Fuel consumption = 7.5 liters/hr

RPM = 2400

Calorific value of fuel = 11400 kcal/kg

Specific gravity of fuel = 0.717

Brake drum diameter = 73.5 cm

Rope diameter = 2.5 cm

Load on brake drum running at one-third engine speed by belts, spring

balances read 60 kg and 8 kg. Mechanical efficiency = 80%

Determine (i) brake thermal efficiency and (ii) indicated mean effective pressure.

73. A full load test on a two-stroke engine yielded the following results:

Speed = 440 rpm

Brake load = 490.5 N

IMEP = 3 bar

Fuel Consumption = 5.4 kg/hour

Rise in jacket water temperature = 36 °C

Jacket water flow = 450 kg/hour

Air fuel ratio by mass = 30 : 1

Temperature of exhaust gas = 360 °C

Temperature of the test room = 19 °C





Barometric pressure = 76 cm of Hg

Cylinder diameter = 22 cm

Stroke = 25 cm

Brake diameter = 1.20 m

Calorific value of fuel = 43000 kJ/kg

Proportion of hydrogen by mass in the fuel = 15%

Given,

Rair = 0.287 kJ/kgK, Cp of water = 4.18 kJ/kgK

Specific heat of dry exhaust gases = 1 kJ/kgK

Specific heat of dry steam = 2 kJ/kgK

Assume enthalpy of superheated steam to be 3180 kJ/kg, Calculate,

(i) the indicated thermal efficiency

(ii) the specific fuel consumption in kg/kWh

(iii) volumetric efficiency based on atmospheric conditions.

Draw up a heat balance for the test on the percentage basis indicating the content

of each item in the balance.

74. Derive an expression for the air-standard efficiency of a Diesel cycle in terms of

the compression ratio (the ratio of the volumes at the beginning and end of the

compression process), the cut-off ratio (ratio of volumes at the end and beginning

of the constant pressure beat addition process) and the ratio of specific heats at

constant pressure and constant volume. Draw a neat sketch of the cycle on the p-

V diagram.

75. An ideal Diesel engine operates with air as the winking substance. The

temperature and pressure of the air at the beginning of the compression process

are 25°C and 1.005 bar. The compression ratio is 18 and the cut-off occurs at 6.5%

of the expansion stroke.

(i) Draw the p-V and the T-s diagrams for the cycle indicating clearly each of

the processes;

(ii) Determine the pressure and temperature at the end of each process;

(iii) Determine the air-standard efficiency of the cycle assuming = 1.4 for air;

(iv) The work done per cycle (assume CP =1.0 kJ/kgK);

The mean effective pressure.

76. An engine working on the ideal Otto cycle takes in air at 1 kg/cm2 and 30°C which

is compressed to 15 kg/cm2 at the end of the compression stroke. The temperature

attained at the end of constant volume heat addition is 900°C. Assuming

adiabatic index to be 1.4 determine (i) the compression ratio, (ii) the thermal

efficiency, (iii) the temperature at the end of compression, (iv) the pressure at the

end of constant volume heating and (v) the mean effective pressure.

77. Show that the temperature at the end of the compression process in an ideal Otto

cycle is the geometric mean of the maximum and minimum temperatures

attained in the cycle if the work done is to be a maximum.

78. The diameter and stroke of a gas engine cylinder are 18 cm and 30 cm

respectively. The ratio of expansion is 5. The pressure and temperature of the

mixture at the beginning of compression are 1.04 kgf/cm2 and 100°C respectively.

Find the index of the compression process and the weight of the mixture in the

cylinder, if the pressure at the end of compression is 7 kgf/cm2. Also calculate the

work done and heat transferred during the process, indicating the direction of





flow. Assume, R = 29.3 kgf-m/kg-K and ratio of specific heats equal to 1.4 for the

mixture.

79. The following data were obtained during the trial of a single cylinder 2-stroke

cycle diesel engine:

Cylinder bore 23 cm; stroke 45 cm; RPM 350; fuel consumed 0.3 kg/min with a

calorific value of 10000 kcal/min; area of indicator diagram 6.0 cm2; length of

diagram 7.8 cm; spring constant 8.5; load on the brake drum 115 kgf at 1.25 m

radius; cooling water used 18 kg/min; temperature of water entering and leaving

18°C; air fuel ratio 28; exhaust gas temperature 410°C; mean specific heat of

exhaust gases 0.25. Calculate: DTP, BHP, mechanical efficiency, indicated

thermal efficiency and brake thermal efficiency.

Also draw up a heat balance sheet on minute basis.

80. The mass analysis of a hydrocarbon fuel is as follows:

C = 84%, H2 = 15% and the balance is incombustible material.

Find (i) mass of air required per kg of fuel for complete combustion, (ii) analysis of

wet exhaust gases, by mass and volume, if 20 kg fuel are supplied, (iii) partial

pressure of the steam formed in the exhaust gases if the total pressure of the

exhaust gases is 1.03 kg/cm2, (iv) heat carried away by dry exhaust gases formed

per kg of fuel if the temperature of exhaust gas is 375°C and the ambient

temperature is 24°C. Take Cp for dry gases = 0.24 kcal/kg°K.

81. A four stroke limited pressure cycle (diesel) engine draws 1.2 kg/ sec of air at 1.03

kg/cm2 and 27°C. Compression ratio of the cycle is 16. Pressure ratio during

constant volume heat addition is 2.0. Total heat added is equal to 550 kcl/kg of air

in the cylinder. Determine (i) pressure, volume and temperature at all salient

points, (ii) % of heat added during constant pressure process, (iii) cut-off ratio,(iv)

thermal efficiency, (v) mean effective pressure.

Represent the cycle on pV and T-s planes. Assume Cp = 0.24 kcal/kg°K and CV =

0.17 kcal/kg°K.

82. A 6-cylinder, four-stroke cycle, 10 cm × 12.5 cm stroke, diesel engine develops 50

kW at 1000 r.p.m. The various efficiencies are mechanical 76%; volumetric 80%

under room conditions; indicated relative 88%; theoretical thermal 52%. The

lower calorific value of the liquid fuel is 45000 kJ. Compute (a) b.m.e.p.; (b) air

fuel ratio; (c) specific fuel consumption.

Assume air density as 0 12 kg/m2 under room conditions.

83. A simple jet carburettor has to supply 5 kg of air per minute. The air is at a

pressure of 1.013 bar and at a temperature of 27°C. Calculate the throat diameter

of the choke for air flow velocity of 90 m/s. Take velocity coefficient to be 0.8.

Assume isentropic flow. Assume the flow lo be compressible.

84. In an I.C. engine operating on the dual cycle (limited pressure cycle), the

temperature of the working fluid (air) at the beginning of compression is 27°C.

The ratio of the maximum and minimum pressures of the cycle is 70 and the

compression ratio is 15. The amounts of heat added at constant volume and at

constant pressure are equal. Compute the air standard thermal efficiency of the

cycle. State three main reasons why the actual thermal efficiency is different from

the theoretical value.

85. The following data refer to a steam turbine power plant employing one stage of

regenerative feed heating:





State of steam entering H.P. stage: 10 MPa, 600°C

State of steam entering LP. stage: 2 MPa, 400°C

State of steam entering condenser: 0.01 MPa, 0.9 dryness fraction.

The correct amount of steam is bled for feed heating at exit from the H.P. stage.

Calculate the mass of steam bled per kg of steam passing through the H.P. stage

and the amount of heat supplied in the boiler per second for an output of 10 MW.

Neglect pump work.

86. A spark-ignition engine, designed to run on octane (C8H18) fuel, is operated on

methane (CH4). Estimate the ratio of the power output of the engine with

methane fuel to that with octane. In both cases the fuel-air ratio is stoichiometric,

the mixture is supplied to the engine at the same conditions, the engine runs at

the same speed, and has the same volumetric and thermal efficiencies. The

heating value of methane is 50,150/kJ/kg while that of octane is 44,880kJ/kg.

87. Prove that for the same compression ratio the Otto cycle is more efficient than the

Diesel cycle.

88. The volume ratios of compression and expansion for a Diesel engine as measured

from an indicator diagram are 15.3 and 7.5 respectively. The pressure and

temperature at the beginning of compression are 1 bar and 27° C. Assuming an

ideal engine, determine the mean effective pressure, the ratio of maximum

pressure to mean effective pressure and the cycle efficiency. Also find the fuel

consumption per kWh if the indicated thermal efficiency is 0.5 of ideal efficiency,

mechanical efficiency 0.8 and calorific value of oil 42000 kJ/kg.

89. During the trial of a single-acting oil engine, cylinder diameter 20 cm, stroke 28

cm, working on the two-stroke cycle and firing every cycle, the following

observations were made:

Duration of trial, 1 hour

Total fuel used, 4.22 kg;

Calorific value,44670 kJ/kg;

Proportion of hydrogen in fuel, 15%

Total number of revolutions, 21000

Mean effective pressure, 2.74 bar

Net brake load applied to a drum of 100 cm diameter, 600N

Total mass of cooling water circulated, 495 kg

Temperature of cooling water: inlet 13° C, outlet 38°C

Air used, 135 kg.

Temperature of air in test room, 20°C and temperature of exhaust gases, 370°C

Assume: Cp gases = 1.005 kJ/kg K and CP steam at atmospheric pressure = 2.093 kJ/kg

K.

Calculate the thermal efficiency and draw up the heat balance.

100. Derive an expression for air standard efficiency of the following cycle in terms of

compression ratio, R, CV and .

(i) an isothermal compression, compression ratio, y

(ii) an increase of pressure at constant volume

an adiabatic expansion.

101. Calculate the percentage loss in the ideal efficiency of a diesel engine with

compression ratio 14 if the fuel cut-off is delayed from 5% to 8%.

102. A 16-cylinder diesel engine has a power output of 800 kW at 900 revolutions per





minute. The engine works on the four stroke cycle and has a fuel consumption of

0.238 kg/kW hr. The pressure in the cylinder at the beginning of injection is 32.4

bar and the maximum cylinder pressure is 55 bar. The injector is set at 214 bar

and maximum pressure at the injector is around 600 bar. The coefficient of

discharge for the injector is 0.6. The specific gravity of the fuel is 0.86. Calculate

the orifice area required per injector if the injection takes place over 10 degree

crank angle.

103. An automobile carburetor having its float chamber vented to the atmosphere is

tested at sea level conditions in the factory without an air cleaner. The main

metering system of this carburetor is found yield a fuel-air ratio of 0.065. The

venture throat pressure is 0.84 bar. This carburetor is now installed in an

automobile and air cleaner is placed on the inlet to carburetor. The air flow rate

with and without the air filter is 230 kg/hr. The pressure drop through the filter is

found to be 0.035 bar at sea level conditions. Assuming z = 0 and orifice coefficient

to be constant calculate

(i) the venturi throat pressure with the air cleaner

(ii) fuel-air ratio with the air cleaner.

Assume incompressible flow.

104. A six cylinder, four stroke spark-ignition engine of 10 cm × 12 cm (bore/stroke)

with a compression ratio of 6 is tested at 4800 rpm on a dynamometer of arm 55

cm. During a 10 minutes test, the dynamometer reads 45 kg and the engine

consumed 5 kg of petrol of calorific value 45 MJ/kg. The carburettor receives the

air at 29⁰C and 1 bar at the rate of 10 kg/min. Calculate:

(i) the brake power

(ii) the brake mean effective pressure

(iii) the brake specific fuel consumption

(iv) the brake specific air consumption

(v) the brake thermal efficiency

(vi) the air-fuel ratio

105. Derive an expression for the diameter of the injector orifice to spray fuel Q

cm3/cycle/cylinder in terms of injection pressure pinj (kN/m2), combustion chamber

pressure pcyl (kN/m2), density of fuel pf(kg/cm3) and period of injection t seconds.

Calculate the diameter of the injector orifice of a six- cylinder, 4-stroke CI engine

using the following data:

Brake power = 250 kW, Engine speed = 1500 r.p.m.; BSFC = 0.3 kg/kW; Cylinder

pressure = 35 bar; Injection pressure = 200 bar; Specific gravity of fuel = 0.88;

Coefficient of discharge of the fuel orifice = 0.92; Duration of injection = 36° of

crank angle.

106. The following data are known for a four cylinder four stroke petrol engine:

Cylinder dimensions: 11 cm bore, 13 cm stroke; engine speed: 2250 rpm; brake

power: 50 kW; friction power: 15 kW; fuel consumption rate: 10.5 kg/h; calorific

value of fuel: 50,000 kJ/kg; air inhalation rate: 300 kg/h; ambient condition: 15° C,

103 bar. Estimate (i) brake mean effective pressure (ii) volumetric efficiency (iii)

brake thermal efficiency, and (iv) mechanical efficiency.

107. Derive an expression for air/fuel ratio of a carburetor by

(i) Neglecting compressibility of air

(ii) Taking compressibility effects into account.

108. A four stroke diesel engine of 3000 cc capacity develops 14 kW per m3 of free air





induced per minute. When running at 3500 rev/min it has a volumetric efficiency

of 85 per cent referred to free air-conditions of 1.013 bar and 27°C. It is proposed

to boost the power of the engine by supercharging by a blower (driven

mechanically from the engine) of pressure ratio 1.7 and isentropic efficiency of 80

per cent. Assuming that at the end of induction the cylinders contain a volume of

charge equal to the swept volume, at the pressure and temperature of the delivery

from the blower, estimate the increase in bp to be expected from the engine. Take

overall mechanical efficiency as 80 per cent, r for air = 1 4, R = 0.287 kJ/kg K.

109. A liquid fuel C7H16 is burned with 10% more air than the stoichiometric air.

Assuming complete combustion, calculate

(i) the mass of air supplied per kg of fuel and

(ii) the volumetric analysis of the dry products of combustion, Assume air

contains 21 per cent O2 by volume.

110. A four - cylinder engine of an automobile is converted to run on propane (C3H8)

fuel. A dry analysis of engine exhaust gives volumetric percentage of CO, CO2 and

O2, respectively at 9.79%, 4.90% and 2.45%. Write the resulting chemical reaction

and find the equivalence ratio.

111. The spark plug is fixed at 18° before top dead centre (TDC) in an SI engine

running at 1800 r.p.m. It takes 8° of rotation to start combustion and get into

flame propagation mode. Flame termination occurs at 12° after TDC. Flame front

can be approximated as a sphere moving out from the spark plug which is offset 8

mm from the centre line of the cylinder whose bore diameter is 8.4 cm. Calculate

the effective flame front speed during flame propagation. The engine speed is

increased to 3000 r.p.m. and subsequently as a result of which the effective flame

front speed increases at a rate such that it is directly proportional to 0.85 times of

engine speed. Flame development after spark plug firing still takes 8° of engine

rotation. Calculate how much engine rotation must be advanced such that the

flame termination again occurs at 12° after TDC.

112. An engine fitted with a single jet carburettor having a jet diameter of 1.25 mm

has a fuel consumption of 6 kg/hr. The specific gravity of fuel is 0.7. The level of

fuel in the float chamber is 5 mm below the top of the jet when the engine is not

running. Ambient conditions are 1 bar and 17°C. The fuel jet diameter is 0.6 mm.

The discharge coefficient of air is 0.85. Air-fuel ratio is 15. Determine the critical

velocity of flow at throat and the throat diameter. Express the pressure at throat

in mm of water column. Neglect compressibility effect. Assume discharge

coefficient of fuel flow is 0.60.

113. Find the percentage increase in the efficiency of a Diesel Cycle having a

compression ratio ‘r’ of 16 and cut off ratio 'rc' is 10% of the swept volume, if Cv

decreases by 2%. Take Cv = 0.717 kJ/kg°K and = 1.4.

114. A four stroke single cylinder petrol engine mounted on a motor cycle was put to

load test. The load measured on dynamometer was 30 kg with drum diameter and

speed respectively at 900 mm and 2000 rpm. The engine consumed 0.15 kg of fuel

in one minute, the calorific value of fuel being 43.5 MJ/kg. The fuel supply to the

engine was stopped and was driven by a motor which needed 5 kW of power to

keep it running at the same speed, the efficiency of the motor being 80%. The

engine cylinder bore and stroke are respectively at 150 mm and 200 mm.

Calculate





(i) brake power,

(ii) Indicated power,

(iii) mechanical efficiency,

(iv) brake thermal efficiency,

(v) Indicated thermal efficiency,

(vi) brake mean effective pressure and

(vii) Indicated mean effective pressure.

115. In an oil engine, working on dual combustion cycle the temperature and pressure

at the beginning of compression are 90°C and 1 bar. The compression ratio is 13 :

1. The heat supplied per kg of air is 1675 kJ, half of which is supplied at constant

volume and half at constant pressure. Calculate (i) the maximum pressure in the

cycle, and (ii) the percentage of stroke at which cut-off occurs.

Take for compression 1.4, R = 0.287 kJ/kgK and C for products of combustion is

0.71 + 20 × 105 T where T is in K.

116. In an air standard Otto cycle the maximum and minimum temperatures are 1400

and 15°C. The heat supplied per kg of air is 800 kJ. Calculate the compression

ratio and cycle efficiency. Also calculate the maximum to minimum pressure ratio

in the cycle.

117. A four cylinder 4 stroke diesel engine has a bore of 212 mm and stroke 292 mm.

At full load at 720 rpm the break mean effective pressure is 5.93 bar and specific

fuel consumption is 0.226 kg/kWH. The air fuel ratio as determined by exhaust

gas analysis is 25 : 1. Calculate the break thermal efficiency and volumetric

efficiency of the engine. Atmospheric conditions are 1.01 bar and 15°C. The

calorific value of fuel may be taken as 44200 kJ/kg.

118. A 100 cc petrol Engine with a compression ratio of 6 compresses the air fuel

mixture to 900 kPa and 375°C. At the end of compression the ignition is started

and the pressure rises along a straight line and attains the highest value of 3.0

MPa after the piston has travelled 4% of the working stroke. The air fuel ratio is

15 :1. Take R for mixture as 0.275 kJ/kg-K, calorific value of fuel = 44 MJ/kg and

Cv = 0.965 kJ/kg-K. Find the heat loss per kg of charge during explosion. Flue

gases and air has same gas constant.

119. A certain mass of air is initially at 260°C and 700 kPa and occupies 0.028 m3. The

air is expanded at constant pressure to 0.084 m3. A polytropic process with n =

1.50 is then carried out, followed by a constant temperature process which

completes the cycle. All the processes are reversible processes.

(i) Sketch the cycle on P-v and T-s coordinates and

(ii) find the efficiency of the cycle.

120. The output of an engine is given as input to an agricultural pump set. The pump

is used for lifting water from a depth of 30 m at the rate of 200 litres/minute. The

transmission efficiency between the engine and the pump is 100% and the pump

is considered to be 100% efficient. The brake thermal efficiency of the engine is

35%, the calorific value of the fuel is 43 MJ/kg, the cost of fuel is Rs 53.00 per litre

and the density of the fuel is 780 kg/m3. Estimate the running cost of the fuel for

1000 m3 of water lifted.

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