ICenginesNumericals (1).pptx .

ICenginesNumericals (1).pptx

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.

3. 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 = 20 o C, Air fuel ratio = 16, Exhaust gas temperature 410 o C, Cp of gas 1.1 kJ/ kg.k , Ambient temperature = 30 C. Calculate the following, 1) IP, 2) BP, 3) Break thermal efficiency and 4) SFC. Also draw a heat balance sheet in kJ/min.

4. Calculation for heat balance Heat supplied by fuel = 4X42,000 / 60= 2800 kJ/min = 100% Heat equivalent of BP = 12.28 X 60 = 736.8 kJ/min = 26.31% Heat carried by cooling water = m w x C pw x(T w2 –T w1 ) = 500 X 4.18X 20/60 = 696.66 kJ/min = 24.88% c. Heat carried by exhaust gas = m g x C pg x( T g - T r ) 1.133 x 1.1 (410 – 30) = 473.59 = 16.91%   m g = m f 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%  

5. Heat Balance sheet Particulars kJ/min % Heat supplied by fuel 2800 100 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

6. 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 = 22 C, Diameter of the break drum = 1.22 m. Calculate, 1) Mechanical efficiency, 2) Break thermal efficiency and 3) Draw the heat balance sheet.

7. Calculation for heat balance A) Heat supplied by fuel = m f 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 = m w x C pw x(T w2 –T w1 ) = 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 % Heat supplied by fuel 367840 100 Heat equivalent of BP 85546.8 23.25 b) Heat carried by cooling water 59774 16.25 c) Heat unaccounted 222519.2 60.5

8. 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 = 27 C, Exit temperature of water = 55 C, Air consumed = 300 kg, Ambient temperature = 30 C, Exhaust gas temperature = 310 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.

9. Calculation for heat balance for minute basis Heat supplied by fuel = 0.133 X 45,000 = 6000 kJ/min = 100% Heat equivalent of BP = 28.745 X 60 = 1,724.7 kJ/min = 28.75% Heat carried by cooling water = m w x C pw x(T w2 –T w1 ) = 550 X 4.18X (55-27)/60 = 1072.86 kJ/min = 17.88 % c. Heat carried by exhaust gas = m g x C pg x( T g - T r ) = 5.133 x 1.1 (310 – 30) = 1580.94 = 26.34%   m g = m f + ma = 0.133 + 5 = 5.133kg/min d. Heat unaccounted = ( 6000 – 1724.7 -1072.86 – 1580.94) = 1,621.5 kJ/min = 27 %  

10. Heat Balance sheet for minute basis. Particulars kJ/min % Heat supplied by fuel 6000 100 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

11. 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 20 C and 40 C respectively. Room temperature = 20 o c, Exhaust gas temperature = 400 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.

12. Calculation for heat balance in kW Heat supplied by fuel = m f X CV = 4 X 43,000/3600= 47.74 kW = 100% Heat equivalent of BP = 11.905 kW = 24.95 % Heat carried by cooling water = m w x C pw x(T w2 –T w1 ) = 500 X 4.18X (40-20)/3600= 11.616 kW = 24.33 % c. Heat carried by exhaust gas = m g x C pg x( T g - T r ) = 0.0366 x 1X (400 – 20) = 13.933 = 29.18% m g = m f + 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 %

13. Heat Balance sheet in kW basis. Particulars kW % Heat supplied by fuel 47.74 100 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

14. 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 10 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 C, Ambient temperature 25 C and pressure 1 bar. Determine, 1) Mechanical efficiency, 2) Thermal efficiency on BP basis, 3) BSFC, 4) P bmep , and Draw the heat balance sheet on percentage.

15. 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 = 30 C, Air-fuel ratio = 22, Exhaust gas temperature = 410 c, Specific heat of exhaurst gas 1.0 kJ/ kg.k , Room temperature = 20 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 .

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

17. Energy Balance sheet in kJ/min basis. Particulars kJ/min % Heat supplied by fuel 1680 100 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