This document contains 7 numerical problems related to performance testing of internal combustion engines. The problems provide data collected during engine tests and ask the reader to calculate various engine performance parameters such as indicated power, thermal efficiency, heat balance, etc. and draw conclusions.

1. Numericals on Performance and Testing of
Internal Combustion Engines

2. 1. In a test of 4 cylinder, 4-stroke petrol engine of 75 mm bore and 100 mm stroke, the
following results were obtained at full throttle at a constant speed and with a fixed setting
of the fuel supply at 0.082 kg/min. BP with all the 4 cylinders working = 15.24 kW, BP with
cylinder No. 1 cutoff = 10.45 kW, BP with cylinder No. 2 cutoff = 10.38 kW, BP with cylinder
No. 3 cutoff = 10.23 KW, BP with cylinder No. 4 cutoff = 10.45. Determine, 1) The indicated
power, 2)The indicated thermal efficiency if the calorific value of fuel = 40 MJ/kg and
Relative efficiency based on I.P, if the clearance volume in each cylinder is 115 CC.

4. 2. The following observations are recorded in a test of one hour duration on a single
cylinder four stroke SI engine. Bore = 220 mm, Stroke = 300 mm, fuel used = 4 kg,
Calorific value of fuel = 42,000 kJ/kg, Speed 300 rpm, MEP = 5 bar, load on break = 60 kg,
Spring balance reading = 30 N, Diameter of break drum = 1.4 m, Quantity of cooling
water = 500 kg, Temperature rise of cooling water = 20o C, Air fuel ratio = 16, Exhaust gas
temperature 410o C, Cp of gas 1.1 kJ/kg.k, Ambient temperature = 30 0 C. Calculate the
following, 1) IP, 2) BP, 3) Break thermal efficiency and 4) SFC. Also draw a heat balance
sheet in kJ/min.

6. Calculation for heat balance
A. Heat supplied by fuel = 4X42,000 / 60= 2800 kJ/min = 100%
a. Heat equivalent of BP = 12.28 X 60 = 736.8 kJ/min = 26.31%
b. Heat carried by cooling water = mw x Cpw x(Tw2 –Tw1) = 500 X 4.18X 20/60 = 696.66
kJ/min = 24.88%
c. Heat carried by exhaust gas = mgx Cpg x(Tg -Tr) 1.133 x 1.1 (410 – 30) = 473.59 = 16.91%
mg = mf x( A/F + 1) / 60 = 4 X (17)/60 = 1.133 kg/min
d. Heat unaccounted = ( 2800 - 736.8 -696.66- 473.59) = 892.95 kJ/min = 31.89%

7. • Heat Balance sheet
Particulars kJ/min %
A)Heat supplied by fuel 2800 100
a) Heat equivalent of BP 736.8 26.31
b) Heat carried by cooling water 696.66 24.88
c) Heat carried by exhaust gas 473.59 16.91
d) Heat unaccounted 892.95 31.89

8. 3. The following observations were made during a one hour test on a single
cylinder four stroke oil engine. Bore = 300 mm, Stroke = 450 mm, Mass of fuel
used = 8.8 kg, Calorific value = 41,800 kJ/kg, Average speed = 200 rpm, Mean
effective pressure = 5.8 bar, Break load = 1860 N, Mass of cooling water
circulated = 650 kg, Temperature rise = 220 C, Diameter of the break drum =
1.22 m. Calculate, 1) Mechanical efficiency, 2) Break thermal efficiency and
3) Draw the heat balance sheet.

10. Calculation for heat balance
A) Heat supplied by fuel = mf X CV = 8.8 X 41,800 =367840 kJ/hr = 100%
a) Heat equivalent of BP = 23.763 X 3600 = 85546.8 kJ/hr = 23.25%
b) Heat carried by cooling water = mw x Cpw x(Tw2 –Tw1) = 650 X 4.18X 22
= 59774 kJ/hr=16.25%
c) Heat unaccounted = (367840 -85546.8 - 59774) = 222519.2 kJ/hr =
60.5%
Heat balance sheet:
Particulars kJ/hr %
A) Heat supplied by fuel 367840 100
a) Heat equivalent of BP 85546.8 23.25
b) Heat carried by cooling water 59774 16.25
c) Heat unaccounted 222519.2 60.5

11. 4. In a test on a three cylinder four stroke internal combustion engine with 22 cm bore and
26 cm stroke. The following data were the observation during a trial period of one hour.
Fuel consumption = 8 kg, Calorific value = 45,000 kJ/kg, Total revolutions of crank shaft =
12,000, Mean effective pressure = 6 bar, Net load on break = 1.5 kN, Break drum diameter=
1.8 m, Rope diameter = 3 cm, Mass of cooling water = 550 kg, Inlet temperature of water =
270 C, Exit temperature of water = 550 C, Air consumed = 300 kg, Ambient temperature =
300 C, Exhaust gas temperature = 3100 C, Specific heat of exhaust gases = 1.1 kJ/kg.K.
Calculate, 1) Indicated and break power in kW, 2) Mechanical Efficiency, 3) Indicated
thermal efficiency and 4) Draw heat balance sheet in kJ/min.

13. Calculation for heat balance for minute basis
A. Heat supplied by fuel = 0.133 X 45,000 = 6000 kJ/min = 100%
a. Heat equivalent of BP = 28.745 X 60 = 1,724.7 kJ/min = 28.75%
b. Heat carried by cooling water = mw x Cpw x(Tw2 –Tw1) = 550 X 4.18X (55-27)/60 = 1072.86 kJ/min
= 17.88 %
c. Heat carried by exhaust gas = mgx Cpg x(Tg -Tr) = 5.133 x 1.1 (310 – 30) = 1580.94 = 26.34%
mg = mf + ma = 0.133 + 5 = 5.133kg/min
d. Heat unaccounted = ( 6000 – 1724.7 -1072.86 – 1580.94) = 1,621.5 kJ/min = 27 %

14. Heat Balance sheet for minute basis.
Particulars kJ/min %
A)Heat supplied by fuel 6000 100
a) Heat equivalent of BP 1724.7 28.75
b) Heat carried by cooling water 1072.86 17.88
c) Heat carried by exhaust gas 1580.94 26.34
d) Heat unaccounted 1621.5 27

15. 5. A test on a 2-stroke oil engine gave the following results at full load, Speed = 350
rpm, Net break load = 650 N, IMEP = 3 bar, Fuel consumption = 4 kg/hr, Jacket cooling
water flow rate = 500 kg/hr, Jacket water temperature at inlet and outlet is 200 C and
400 C respectively. Room temperature = 20o c, Exhaust gas temperature = 4000 C, Air
used per kg of air fuel = 32, Cylinder diameter = 22 cm, Stroke = 28 cm, Break = drum
circumference 314 cm. Calorific value of fuel = 43 MJ/kg, Mean specific heat of
exhaust gases = 1 kJ/kg.k. Determine 1) Mechanical efficiency 2) BMEP and 3) Draw
heat balance sheet in kw and in percentage.

17. • Calculation for heat balance in kW
A.Heat supplied by fuel = mf X CV = 4 X 43,000/3600= 47.74 kW = 100%
a. Heat equivalent of BP = 11.905 kW = 24.95 %
b. Heat carried by cooling water = mw x Cpw x(Tw2 –Tw1) = 500 X 4.18X (40-
20)/3600= 11.616 kW = 24.33 %
c. Heat carried by exhaust gas = mgx Cpg x(Tg -Tr) = 0.0366 x 1X (400 – 20)
= 13.933 = 29.18%
mg = mf + ma = 4+(32 X4 + 5 = 5.133kg/min
d. Heat unaccounted = ( 47.74 – 11.905-11.616- 13.933) = 10.336 kJ/min
= 21.65 %

18. Heat Balance sheet in kW basis.
Particulars kW %
A)Heat supplied by fuel 47.74 100
a) Heat equivalent of BP 11.905 24.95
b) Heat carried by cooling water 11.616 24.33
c) Heat carried by exhaust gas 13.933 29.18
d) Heat unaccounted 10.336 21.65

19. 6. The following readings were recorded during a trial on a single cylinder two stroke diesel
engine. Power developed by electric motor for motoring at rated speed = 1.5 kW, Rated
speed 500 rpm, Net load on break 225 N, Diameter of break wheel 100 cm, Rate of cooling
water through engine jacket 13.65 kg/min, Rise in temperature of cooling water 100 c, Fuel
consumption 2 kg/hr, CV of the fuel 43,000 kJ/kg, Air fuel ratio 32, Cp of gases 1.006
kJ/kg.K, Exhaust gas temperature 345 0 C, Ambient temperature 250 C and pressure 1 bar.
Determine, 1) Mechanical efficiency, 2) Thermal efficiency on BP basis, 3) BSFC, 4) Pbmep,
and Draw the heat balance sheet on percentage.

24. 7. A test on a single cylinder, 4-stroke oil engine having a bore of 15 cm and stroke 30 cm
give the following results. Speed = 300 rpm, Break torque = 200 N-m, Indicated mean
effective pressure = 7 bar, Fuel consumption = 2.4 kg/hr, Cooling water flow =5 kg/min,
Cooling water temperature rise = 300 C, Air-fuel ratio = 22, Exhaust gas temperature = 4100
c, Specific heat of exhaurst gas 1.0 kJ/kg.k, Room temperature = 200 C, Room pressure = 1
bar, Calorific value of fuel 32MJ/kg, Gas constant R= 0.2872 kJ/kg.k. Determine, 1) Indicated
thermal efficiency, 2) Volumetric efficiency based on atmospheric conditions, 3) Draw an
energy balance sheet in terms of kJ/min and percent basis.

27. 2) Heat equivalent of BP = 376.8 kJ/min

28. Energy Balance sheet in kJ/min basis.
Particulars kJ/min %
A)Heat supplied by fuel 1680 100
a) Heat equivalent of BP 376.8 23.55
b) Heat carried by cooling water 627.3 37.34
c) Heat carried by exhaust gas 343.2 20.42
d) Heat unaccounted 332.7 19.80