Me-413 Internal Combustion Engine Problem Set 3 Name: Year & Section

ME-413 INTERNAL COMBUSTION ENGINE PROBLEM SET 3 Name: Year & Section: 1. An ideal Diesel engine operates on 1 ft^3 (measured at state 1) of air. Let P1=14.4 psia, T1= 140 deg F, rk=14 and let the cut off be at 6.2% of the stroke. Draw the PV and TS diagrams, use the air properties, and find: a.

T2, P2, V2

b. T3, V3 c.

P4, T4

d. Heat absorbed e. Heat Rejected f.

Work

g.

Efficiency

h. Mean Effective Pressure 2. Determine the air-standard efficiency of an engine operating on the Diesel cycle when the suction pressure is 99.97kPa and the fuel is injected for 6% of the stroke, the clearance volume is 8% of the stroke. Assume k= 1.4. 3. In an air standard Diesel cycle, compression starts at 100kPa and 300K. The compression ratio is 16 to 1. The maximum cycle temperature is 2031K. Determine the thermal efficiency. 4. A Diesel engine is operating on a 4-stroke cycle, has a heat rate of 11,315.6 kJ/kW-hr brake. The compression ratio is 13. The cut-off ratio is 2. Using k = 1.32 what is the brake engine efficiency 5. There are supplied 400kJ per cycle to a Diesel engine operating on 500g air, P1 = 100kPa T1 = 50 deg C. At the end of compression, P2 = 4000kPa. Determine the effective pressure of the engine. 6. The compression ratio in a Diesel engine is 13 to 1 and the ratio of expansion is 6.5 to 1. At the beginning of compression the temperature is 32˚C. Assuming adiabatic compression and expansion calculate the ideal thermal efficiency taking the specific heats and constant pressure and volume as 1.005kJ/kg-K and 0.718kJ/kg-K respectively. 7. The ratio of compression in a Diesel engine is 16 to 1 and the temperature of the air at the beginning of the compression ratio is 49oC. Calculate the temperature at the end of compression assuming it follows the law PV1.34= C. 8. The pressure and temperature of the air at the beginning of compression in a diesel engine is 111.46kPa and 35oC respectively, and the clearance volume is equal to 7.5% of the piston swept volume. Calculate the pressure at t he end of compression assuming the law of compression if PV1.36 = C. 9. When the piston is moving up in a two-stroke diesel engine, the scavenge ports are closed when the piston is 675mm from the top of its stroke, the pressure and temperature of the air in the cylinder then being 13.80kPag and 43oC. The clearance is equal to 65mm and the diameter of the cylinder is 650mm. Calculate the mass of air compressed in the cylinder taking the atmospheric pressure as 101.325kPa and R for air as 0.287kJ/kg-K. 10. The compression ratio of a compression-ignition engine is 14 to 1. The diameter of the cylinder is 500mm and the stroke to bore ratio is 1.2 to 1. At the beginning of the compression the pressure and

temperature of the air in the cylinder is 105kPa and 51 oC, and the compression follows the law PVn = C, where n = 1.35. Calculate the work done on the air during compression. 11. If the volumes at the end of compression and at the beginning of expansion in an ideal Diesel engine are 0.015m3 and 0.040m3 respectively. What is the cut-off ra tio? 12. If the compression ratio and the cut-off ratio of a Diesel engine are 15 and 3 respectively, what is the expansion ratio? 13. What is the efficiency of the Diesel engine if the heat added during the constant pressure combustion is 19 BTU and the heat rejected is 9 BTU. 14. A diesel cycle operates with a compression ratio of 14 and with a cut-off occurring at 5% of the stroke. Find the cut-off ratio, if the initial volume is 1.5ft3. 15. The compression ratio and the cut-off ratio of an ideal diesel cycle are 13 and 3 respectively. What is the cycle efficiency for a cold-air standard value of k. 16. A diesel engine takes in air at 105kPa and 26oC subjected to a compression ratio of 19. What is the operating clearance in percent? 17. The volumes of states 1,2 and 3 of a diesel cycle operating on a hot air standard are 300cm 3, 30cm3, 90cm3 respectively. Find the power output if t he heat input is 120kW. 18. An ideal diesel engine operates on a 1kg of cold air with a suction pressure of 110kPa and an initial temperature of 40oC. The compression pressure is 3000kPa and the cut-off ratio is at 8% of the stroke from head-end to dead-end center of the piston. Calculate the ideal cycle t hermal efficiency.