# Problems on Internal Combustion Engines Engine Fundamentals

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1 Problems on Internal Combustion Engines Engine Fundamentals 1. A four-stroke SI engine delivers a brake power of 442 kw with a mechanical efficiency of 85 %. The measured fuel consumption is 160 kg of fuel in one hour and air consumption is 410 kg during one sixth of an hour. The heating value of the fuel is kj/kg. Calculate (i) indicated power, (ii) frictional power, (iii) air-fuel ratio, (iv) indicated thermal efficiency and (v) brake thermal efficiency. [520 kw, 78 kw, 15.37, 0.278, 0.236] 2. A spark-ignition engine has a fuel-air ratio of How many kgs of air per hour are required for a brake power output of 73.6 kw at an overall brake thermal efficiency of 20 %. How many m 3 of air are required per hour if the density of air is kg/m 3. If the fuel vapour has a density four times that of air, how many m 3 per hour of the mixture is required? The calorific value of the fuel is kj/kg. [ m 3 /hr, m 3 /hr] 3. The engine of the Fiat car has four cylinders of 68 mm bore and 75 mm stroke. The compression ratio is 8. Calculate the cubic capacity of the engine and the clearance volume of each cylinder. [ cm 3, 38.9 cm 3 ] 4. A twin-cylinder two-stroke engine has a swept volume of 150 cm 3. The maximum power output is 19 kw at rpm. At this condition, the bsfc is 0.11 kg/mj, and the gravimetric air/fuel ratio is 12:1. If the ambient test conditions were 10 0 C and 1.03 bar, and the fuel has a calorific value of 44 MJ/kg, calculate the bmep, the brake thermal efficiency and the volumetric efficiency. [6.91 bar, 20.6 %, 72 %] 5. The Rolls Royce CV12 turbocharged four-stroke direct injection diesel engine has a displacement of 26.1 litres. The engine has a maximum output of 900 kw at 2300 rpm and is derated to kw at 1800 rpm for industrial use. What is the bmep for each of these types? [18 bar, bar] 6. The high performance version of the CV12 has a bsfc of kg/mj at maximum power, and a minimum bsfc 0f kg/mj. Calculate the brake thermal efficiencies for both conditions, and the fuel flow rate at maximum power. The calorific value of the fuel is 42 MJ/kg. [37.79 %, %, kg/s] 7. During the power stroke of an engine, the gas pressure force acting on the piston is transmitted to the crankshaft via the connecting rod. List the forces acting on the piston during this part of the operating cycle. Show the direction of the forces acting on the piston in a piston, cylinder, connecting rod and crank mechanism. Write out the force balance for the piston (a) along the cylinder axis and (b) transverse to the cylinder axis in the plane containing the connecting rod. 8. Suggest reasons why multi-cylinder engines prove more attractive than single cylinder engines once the total engine displaced volume exceeds a few hundred cubic centimeters. 9. State the impact on airflow, maximum torque and maximum power when there is a change in a spark ignition engine from 2 valves per cylinder to 4 valves (2 inlet and 2 exhaust) per cylinder. 10. What are the advantages of over square and under square engines?

2 Engine Parameters 11. A six-cylinder diesel engine with displaced volume of 10 litres operates at 2100 rpm and with mean piston speed of 8 m/s. Calculate the airflow if volumetric efficiency is If F/A ratio is 0.05, what is the fuel flow rate, and mass of fuel injected per cylinder per cycle? [190 gm/s, 76 mg/cycle/cylinder] 12. A pickup truck has a five-litre, V6, SI engine operating at 2400 rpm. The engine has a compression ratio of 10.2:1 and its volumetric efficiency is The bore and the stroke are related as L=0.92B. Calculate (a) stroke length, (b) average piston speed, (c) clearance volume of one cylinder and (d) airflow rate into the engine. [9.65 cm, 7.72m/s, 90.6 cm 3, kg/s] 13. A six cylinder two-stroke engine produces a torque of 1100 Nm at a speed of 2100 rpm. It has a bore of 123 mm and a stroke of 127 mm. What is its bmep and mean piston speed? [7.63 bar, 8.89 m/s] 14. A 380 cc single-cylinder two-stroke motorcycle engine is operating at 5500 rpm. The engine has a bore of 82 mm and stroke of 72 mm. Performance testing gives a bmep of 6.81 bar, bsfc of 0.49 kg/kw hr, and a delivery ratio of Calculate the fuel to air ratio and the airflow rate. [30.48 gm/s, 0.106] 15. A single-cylinder, two-stroke cycle model airplane engine with 7.54 cm 3 displacement produces 1.42 kw of brake power at 23,000 RPM. The square engine (B=L) uses 31.7 gm/min of castor oil-methanol-nitromethane fuel at an air-fuel ratio AF=4.5. During intake scavenging, 65 % of the incoming air-fuel mixture gets trapped in the cylinder, while 35 % of it is lost with the exhaust before the exhaust port closes. Assuming combustion efficiency of 94 %, calculate (a) brake specific fuel consumption, (b) average piston speed, (c) unburnt fuel exhausted to atmosphere and (d) torque. [1339 gm/kw-hr, m/s, 12.3 gm/min, 0.59 N-m] 16. The power per unit piston area (termed as specific power) is a measure of the designer s success in using the available piston area regardless of size. Derive an expression for specific power in terms of mep and mean piston speed for twostroke and four-stroke cycles. 17. Explain why the bmep of a naturally aspirated diesel engine is lower than that of a naturally aspirated spark-ignition engine. Explain why the bmep is lower at the maximum rated power for a given engine than the bmep at the maximum torque. 18. The values of mep at rated speed, maximum mean piston speed, and maximum specific power are essentially independent of cylinder size for naturally aspirated engines of a given type. If we also assume that engine weight per unit displaced volume is essentially constant, how will the specific weight of an engine at fixed total displaced volume vary with the number of cylinders? Assume the bore and stroke are equal. Air standard Cycles 19. An engine working on the Otto cycle is supplied with air at 0.1 Mpa and 35 0 C. The compression ratio is 8. Heat supplied is 2100 kj/kg. Calculate the maximum pressure and temperature of the cycle, the cycle efficiency, and the mean effective pressure.

3 20. A diesel engine has a compression ratio of 14 with cut-off volume at 6 % of the stroke. Calculate the air standard efficiency. 21. In an air standard diesel cycle, the compression ratio is 16, and at the beginning of isentropic compression, the temperature is 15 0 C and the pressure is 0.1 Mpa. Heat is added until the temperature at the end of the constant pressure process is C, calculate (a) the cut-off ratio, (b) the heat supplied per kg of air, (c) the cycle efficiency and (d) the mean effective pressure. 22. An air standard dual cycle has a compression ratio of 16, and compression begins at 1 bar, 50 0 C. The maximum pressure is 70 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Estimate (a) the pressure and temperature at cardinal points of the cycle, (b) the cycle efficiency, and (c) the mep of the cycle. 23. In the pressure-volume diagram of an Otto cycle, assume that expansion stroke continues until the pressure is atmospheric. Derive an expression for the efficiency for a complete expansion cycle in terms of γ, α=v4/ V3 and β= V1/ V In the Otto cycle, all the heat transfer occurs at constant volume. It is more realistic to assume that part of heat transfer occurs after the piston has started its downward motion in the expansion stroke. Therefore, consider a cycle identical to the Otto cycle except that the first two-third of the total heat transfer occurs at constant volume and last one-third occurs at constant pressure. Assume that total heat transfer is 2100 kj/kg, and that the state at the beginning of the compression process is 90 kpa and 20 0 C, and that the compression ratio is 9. Calculate the maximum pressure and temperature and the thermal efficiency of this cycle. Compare the results with those of a conventional Otto cycle having the same given variables. 25. Explain why air-standard cycles are used to represent the performance of real internal combustion engines. 26. Outline the shortcomings of the simple ideal cycles, and explain how the fuel-air cycles and computer models overcome these problems. 27. Explain why constant-volume combustion gives a higher indicated thermal efficiency than constant-pressure combustion for the same compression ratio. Fuel Air Cycles 28. A constant volume fuel-air cycle uses air-fuel ratio 15:1. The fuel has a heating value of 42 MJ/kg. The compression ratio is 9, and the residual gas fraction is Pressure and temperature at the start of compression process is 1 bar and 360 K. Estimate the efficiency of the cycle, taking the index of compression and expansion to be 1.3, and the average cv = kj/kg K. Also, calculate the ideal Otto cycle efficiency. [48.26 %, %] 29. In a diesel engine, combustion is assumed to begin at inner dead center and to be at constant pressure. The air-fuel ratio is 28:1, the calorific value of the fuel is kj/kg and the specific heat of products of combustion is given by cv = x 10-5 T and R for the products = kj/kg K. If the compression ratio is 14:1, and the temperature at the end of compression is 800 K, find at what percentage of the stroke, combustion is completed. [18.65 %]

4 30. What is the effect of percentage change in the efficiency of Otto cycle having a compression ratio of 7, if the specific heat at constant volume increases by 1 %. [ %] 31. A petrol engine of compression ratio 6 uses a fuel of calorific value kj/kg. The fuel air ratio is 15:1. The temperature and pressure of the charge at the end of the suction stroke are 333 K and 1 bar respectively. Estimate the maximum pressure in the cylinder if the index of compression is 1.32 and the specific heat at constant volume is expressed by the relation cv = x 10-5 T kj/kg K, where T is the temperature in K. Compare this value with that of constant specific heat cv =0.71 kj/kg K. [56.6 bar, 80.5 bar] 32. An engine working on dual combustion cycle, the temperature and pressure at the beginning of compression are 363 k 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 k for compression = 1.4, R = kj/kg K and cv for products of combustion to be x 10-5 T. [66.2 bar, 2.64 % of stroke] 33. What is the effect on the efficiency of a Diesel cycle having a compression ratio of 20, with cut-off ratio at 5 % of the swept volume, if the specific heat at constant volume increases by 1%. Take cv = kj/kg K and R = kj/kg K. [-565 %] 34. How do the specific heats vary with temperature? What is the physical explanation for this variation? Carburettor 35. A four-stroke, four-cylinder engine with a total displaced volume of m 3 running at 2000 rpm has a carburetor venturi with a 3 cm throat. Determine the suction at the throat assuming volumetric efficiency of the engine to be 70 %. Assume density of air to be 1.2 kg/m 2 and coefficient of airflow 0.8. [0.339 bar] 36. A petrol engine consumes 7.5 kg of petrol per hour. The specific gravity of fuel is The air temperature is 298 K. The air fuel ratio is 15. The choke tube has a diameter of 22 mm. Calculate the diameter of the fuel jet of a simple carburetor. The top of jet is 4 mm above the petrol level in the float chamber. Take coefficient of discharge as 0.82 and 0.7 for air and fuel respectively. Assume atmospheric pressure = bar. [1.244 mm] 37. Determine the change of air-fuel ratio in an aircraft carburetor when it takes off from sea level to a height of 5000 m. Carburetor is adjusted for 15:1 ratio at sea level where the air temperature is 27 0 C and pressure 1 bar. Assume the variation of temperature of air with altitude at t=ts h, where h is in metres and t is in 0 C. The air pressure decreases with altitude as per relation h = log10 (1/p), where p is in bar. Calculate the air-fuel ratio at the altitude of 5000 m. [11.77] 38. A carburetor, tested in a laboratory has its float chamber vented to atmosphere. The main metering system is adjusted to give an air-fuel ratio of 15:1 at sea level conditions. The pressure at the venturi throat is 0.8 bar. The atmospheric pressure is 1 bar. The same carburetor is tested again when an air cleaner is fitted at the inlet to the carburetor. The pressure drop to air cleaner is found to be 30 mm Hg when airflow at sea level condition is 240 kg/h. Assuming zero lip and constant coefficient

5 of flow, calculate (i) the throat pressure when the air cleaner is fitted and (ii) air-fuel ratio when the air cleaner is fitted. [0.76 bar, 13.7] 39. A 4-cylinder, 4-stroke Ambassador car has a capacity of 1490 cm 3. It develops a maximum power at 4200 rpm and air-fuel ratio required is 13:1. The volumetric efficiency of the engine=0.70. The air speed at venturi is limited to 90 m/s and nozzle has a lip of 6 mm. Assuming coefficient of discharge for the venturi to be 0.85, and that for the nozzle 0.66 and density of fuel=740 kg/m 3, calculate the diameter of the venturi and the nozzle. An allowance is to be made for the capillary tube whose diameter should be taken as 0.4 times the venturi diameter. Atmospheric pressure and temperature are bar and 293 K. [2.74 cm, 1.56 mm] 40. Explain why a rich mixture is required for idling? 41. Explain the advantages of having a multi-barrel carburetor. 42. Port fuel-injection systems are replacing carburetors in automobile spark-ignition engines. List the major advantages/disadvantages of fuel metering with port fuel injection relative to carburetor. Fuel Injection Systems 43. A six-cylinder, four-stroke diesel engine develops 125 kw at 3000 rpm. Its brake specific fuel consumption is 200 gm/kw h. Calculate the mass of fuel to be injected per cycle per cylinder. [ gm] 44. An automobile has a 3.2 litre, five cylinder, four stroke cycle diesel engine operating at 2400 rpm. Fuel injection occurs from 20 0 btdc to 5 0 atdc. The engine has a volumetric efficiency of 0.95 and operates with fuel equivalence ratio of Light diesel fuel having stoichiometric air-fuel ratio 14.5 is used. Calculate (i) time for one injection and (ii) fuel flow rate through an injector. [ sec/injection, kg/s] 45. A diesel engine with bore B=8.2 cm has the fuel injectors mounted at the center of the cylinder head. The injectors have a nozzle diameter of mm, a discharge coefficient of 0.72, and an injection pressure of 50 Mpa. Average cylinder pressure during injection can be considered as 5000 kpa. Density of the diesel fuel is 860 kg/m 3. Calculate (i) average velocity of the fuel jet as it leaves the injector and (ii) time for a fuel particle to reach the cylinder wall if it travels at average exit velocity. [233 m/s, sec] 46. Calculate the diameter of the fuel orifice of a 4-stroke engine that develops 25 kw per cylinder at 2500 rpm. The specific fuel consumption is 0.3 kg/kwh. The fuel is injected at a pressure of 150 bar over a crank travel of The pressure in the combustion chamber is 40 bar. The coefficient of velocity is and specific gravity of fuel is [0.793 mm] 47. A single cylinder 4-stroke oil engine develops 20 kw at 1200 rpm. Its specific fuel consumption is 300 gms/kwh. The fuel density is 860 kg/m 3. The fuel injection is carried out during 30 0 rotation of crank. The average fuel injection pressure and chamber pressure are 120 bar and 30 bar. Find the diameter of the nozzle if four orifices are used in the nozzle. Assume cofficient of discharge=0.65. [0.4 mm] 48. At injection pressure of 150 bar a spray penetration of 25 cm in 20 milliseconds is obtained. If an injector pressure of 250 bar had been used, what would have been the time taken to penetrate the same distance. Assume the same orifice and

6 combustion chamber density. The combustion chamber pressure is 25 bar. Use the relation, S α t p where, S = penetration in cm, t = time in milliseconds and p = pressure difference between injection pressure and combustion chamber pressure. [14.91] 49. What is purpose of using a governor in CI engines? Explain the working principle of any one-type of governor. 50. With sketches, explain the types of fuel nozzles used in CI engines. Supercharger and Turbocharger 51. A 5.6 litre V8 engine with a compression ratio of 9.4:1 operates on an air-standard Otto cycle at 2800 RPM, with a volumetric efficiency of 90 % and a stoichiometric air-fuel ratio using gasoline. The exhaust flow undergoes a temperature drop of 44 0 C as it passes through the turbine of the supercharger. Calculate (a) mass flow rate of exhaust gas and (b) power available to drive the turbocharger compressor. [0.148 kg/s, 7.22 kw] 52. Two identical motorcars fitted with 4-stroke engines of the same dimensions and having swept volume of 3300 cc. One engine is normally aspirated and develops a bmep of 9.3 bar at 4500 rpm, its indicated thermal efficiency being 28.5 % and its mechanical efficiency 90 %. The other engine is fitted with a supercharger and develops a bmep of 12.1 bar at 4500 rpm (its compression ratio being lowered to avoid detonation); its indicated thermal efficiency is 24.8 % and its mechanical efficiency 90 %. The mass of the unboosted engine is 205 kg and that of the boosted engine (with accessories) is 225 kg. If both the cars are supplied with sufficient petrol for a test of H hours duration, what is the maximum value of H if the specific mass (i.e., the ratio of mass of engine plus fuel to bp) of the boosted engine is always to be less than that of the unboosted one. The fuel used for both the cars is the same and its calorific value is kj/kg. [5.87 hours] 53. The entire output of a supercharged four-stroke cycle oil engine is used to drive an air compressor 293 K, and is delivered to a cooler which removes heat at the rate of 1340 kj/min. the air leaves the cooler at 333 K and 1.72 bar. Part of this air flow is used to supercharge the engine which has a volumetric efficiency of 0.70 based on induction manifold condition of 333 K and 1.72 bar. The engine, which has six cylinders of 90 mm bore, and 100 mm stroke runs at 2000 rpm and delivers an output torque of 147 N-m. The mechanical efficiency of the engine is Determine (a) the engine imep, (b) the air consumption in kg/min, and (c) the airflow into the compressor in kg/min. [6.45 bar, 4.8 kg/min, 12.6 kg/min] 54. A diesel engine is fitted with a turbocharger, which comprises a radial compressor driven by a radial exhaust turbine. The air is drawn into the compressor at a pressure of 0.95 bar and at a temperature of 288 K, and is delivered to the engine at a pressure of 2.0 bar. The engine is operating on a gravimetric air/fuel ratio of 18:1, and the exhaust leaves the engine at a temperature of 873 K, and at a pressure of 1.8 bar; the turbine exhaust at 1.05 bar. The isentropic efficiencies of compressor and turbine are 70 % and 80 % respectively. Using the values Cp for air = 1.01 kj/kg K, γ = 1.4; and Cp for exhaust gas = 1.15 kj/kg K, γ = 1.33, calculate (i) the temperature of the air leaving the compressor, (ii) the temperature of the gases

7 leaving the turbine, and (iii) the mechanical power loss in the turbocharger expressed as a percentage of the power generated in the turbine. [372 K, 785 K, 7.34 %] 55. Compare the cooling effect of fuel evaporation on charge temperature in a turbocharged SI engine for the following two cases: (a) the carburetor placed before the compressor, (b) the carburetor placed after the compressor. The specific heat capacity of the air and latent heat of evaporation of the fuel are both constant. For the air/fuel ratio of 12.5 :1, the evaporation of the fuel causes a 25 K drop in mixture temperature. The compressor efficiency is 70 % for the pressure ratio of 1.5, and the ambient air is at 288 K. Assume Cp for air = 1.01 kj/kg K, γ = 1.4; Cp for air/fuel mixture = 1.05 kj/kg K, γ = Finally, compare the compressor work in both cases. [303.7 K, K, kj/kg, kj/kg] 56. An eight-cylinder turbocharged aftercooled four-stroke cycle diesel engine operates with an inlet pressure of 1.8 atmosphere at its maximum rated power at 2000 rpm. Bore and strokes of the engines are 128 mm and 140 mm respectively, and volumetric efficiency based on inlet manifold conditions of 1.8 atm and 325 K after the aftercooler is 0.9. The compressor isentropic efficiency is 0.7. Calculate (a) the power required to drive the turbocharger compressor, (b) the pressure at the turbine inlet if the exhaust gas temperature is 923 K and the turbocharger isentropic efficiency is 0.65, and the turbine exhausts to the atmosphere. Assume a fuel-air ratio of 0.035, and the following property values: Cp for air = 1.00 kj/kg K, γ = 1.4; Cp for gas = 1.25 kj/kg K, γ = [33 kw, atm] 57. (a) Why is the compression ratio of an SI engine often reduced when the engine is redesigned to be used with a turbocharger? (b) Is brake power increased or decreased? (c) Why isn t reducing the compression ratio as important when a turbocharger is added to a CI engine design? 58. What are the advantages and disadvantages in using an inter-cooler? Explain under what circumstances it should be used? 59. What is a two-stage supercharging? 60. What do understand by the term turbo-lag? In-cylinder Fluid Motion 61. A 150 in 3, 4-cylinder, 4-stroke cycle, high swirl CI engine is running at 3600 RPM. Bore and stroke are related by S=0.95 B. During the compression stroke, the cylinder air has a swirl ratio of 8. Calculate (a) swirl tangential speed and (b) angular velocity of cylinder air using the paddle-wheel model. [281 ft/s, 291 rev/s] 62. A 2.4 litre, 3-cylinder, 4-stroke cycle SI engine with a 9.79 cm stroke is running at 2100 RPM. During the compression stroke, the air-fuel mixture has a swirl ratio (angular speed/engine speed) of 4.8. At TDC, the mixture (that consists of kg in each cylinder) is compressed into a clearance volume that can be approximated as a cylindrical bowl in the face of the piston as shown in the following figure. It can be assumed that angular momentum is conserved. Calculate (a) angular speed of swirl at TDC, (b) tangential speed at the outer edge of the bowl at TDC, and (c) swirl ratio at TDC in terms of tangential speed and piston speed. [485.2 rev/s, m/s, 13.3]

8 63. The crevice volume of an engine equals 2 % of the total clearance volume. It can be assumed that pressure in the crevices is about the same as in the combustion chambe r, but the temperature stays at the cylinder wall temperature of C. Cylinder inlet conditions are 60 0 C and 98 kpa, and the compression ratio is 9.6:1. It can be assumed that only 80 % of fuel trapped in the crevice volume gets burned later in the power stroke. Calculate (a) what % of the fuel is trapped in the crevices at the end of compression stroke, and (b) what % of the fuel ends up in the exhaust due to being trapped in the crevice volume. Assume γ=1.35. [3.138 %, %] 64. A 6.8 litre, in-line, eight cylinder CI engine has a compression ratio of 18.5 and a crevice volume equal to 3 % of the clearance volume. During the engine cycle pressure in the crevice volume equals combustion chamber pressure while remaining at the cylinder wall temperature of C. Cylinder conditions at the start of compression are 75 0 C and 120 kpa, and peak pressure is 11,000 kpa. Cut-off ratio is 2.3. Calculate (a) crevice volume in the cylinder, (b) % of air-fuel mixture in the crevice volume at the end of compression, and (c) % of air-fuel mixture in the crevice volume at the end of combustion. Assume γ=1.35. [1.457 cm 3, 5.88 %, %] 65. Derive a relationship for the depth hb of a disc shaped bowl-in-piston direct injection diesel engine combustion chamber in terms of compression ratio (rc), bore (B), stroke (L) and bowl diameter (DB), and top-centre cylineder-head to pistoncrown clearance (c). For B=L=100 mm, rc=16, DB=0.5B, c=1 mm, find the fraction of air charge within the bowl at TDC. 66. What do you understand by reverse squish and reverse blowby? Combustion 67. The spark plug is fired at 18 0 btdc in an engine running at 1800 RPM. It takes 8 0 of engine rotation to start combustion and get into flame propagation mode. Flame termination occurs at 12 0 atdc. Bore diameter is 8.4 cm and the spark plug is offset 8 mm from the centerline of the cylinder. The flame front can be approximated as a sphere moving out from the spark plug. Calculate the effective flame front speed during the flame propagation. [24.5 m/s] 68. The engine in problem-67 is now run at 3000 RPM. As speed is increased in this engine, greater turbulence and swirl increase the flame front speed at a rate such that effective flame speed is proportional to 0.85 N. Flame development after spark plug firing still takes 8 0 of engine rotation. Calculate how much ignition timing must be advanced such that flame termination again occurs at 12 0 atdc. [ ] 69. An automobile has a 3.2-litre, five-cylinder, four-stroke cycle engine operating at 2400 RPM. Fuel injection occurs from 20 0 btdc to 5 0 atdc. The engine has a compression ratio of 18:1 and operates on an air-standard Dual cycle. At 2400 RPM, combustion starts at 7 0 btdc and lasts for 42 0 of engine rotation. The ratio

9 of connecting rod length to crank offset is R=3.8. Calculate (a) ignition delay and (b) cycle cut-off ratio. [13 0, 2.91] 70. A CI engine with a 3.2-inch bore and 3.9-inch stroke operates at 1850 RPM. In each cycle, fuel injection starts at 16 0 btdc, and lasts for second. Combustion starts at 8 0 btdc. Due to higher temperature, the ignition delay of any fuel injected after combustion starts is reduced by a factor of two from the original ID. Calculate (a) ID of first fuel injected in second, (b) ID of first fuel injected in degrees of engine rotation and (c) crank angle position when combustion starts on last fuel droplets injected. [ sec, 8 0, ] 71. A 3.2-litre SI engine is to be designed with bowl-in-piston combustion chambers. With a central spark plug and combustion at TDC, this gives a flame travel distance of B/4, where B is the bore. The engine is to operate with an average piston speed of 8 m/s and burn angle of 25 0 of engine rotation. Stroke and bore are related by S=0.95 B. Calculate (a) average flame speed if the design is for an in-line four cylinder engine, and (b) average flame speed if the design is for a V8 engine. [15.2 m/s, 15.2 m/s] 72. A large CI engine operating at 310 RPM has open combustion chambers and direct fuel injection, with 26-cm bore, a 73-cm stroke, and compression ratio of 16.5:1. Fuel injection in each cylinder starts at 21 0 btdc and lasts for second. ID is second. Calculate (a) ID in degrees of engine rotation, (b) crank angle position when combustion starts and (c) crank angle position when injection stops. [12.1 0, btdc, atdc] Intake and Exhaust Valves 73. A 2.8 litre, four-cylinder square engine (bore=stroke) with two intake valves per cylinder is designed to have a maximum speed of 7500 RPM. Intake temperature is 333 K. Calculate (a) intake valve area, (b) diameter of intake valves and (c) valve lift. [7.913 cm 2, 2.24 cm, cm] 74. A V8 engine with 7.5 cm bores is redesigned from two valves per cylinder to four valves per cylinder. The old design had one inlet valve of 34 mm diameter and one exhaust valve of 29 mm diameter per cylinder. This is replaced with two inlet valves of 27 mm diameter and two exhaust valves of 23 mm diameter. Maximum valve lift equals 22 % of the valve diameter for all valves. Estimate the increase of inlet flow area per cylinder when the valves are fully open. Also state the advantages/disadvantages of the new system. [2.087 cm 2 ] 75. A 3.6 litre, V6 SI engine is designed to have a maximum speed of 7000 RPM. There are two intake valves per cylinder, and valve lift equals one-fourth valve diameter. Bore and strokes are related as S = 1.06 B. Design temperature of the air-fuel mixture entering the cylinder is 333 K. Calculate (a) ideal theoretical valve diameter, (b) maximum flow velocity through the intake valve and (c) do the valve diameters and bore size seem compatible? [2.0 cm, m/s] 76. Two possible overhead valve combustion chambers are considered, the first has two valves and the second design has four valves per cylinder. The diameter of the inlet valve is 23 mm for the first design, and 18.5 mm for the second design. If the second design is adopted, what is the % increase in total inlet valve perimeter? If the valve lift is restricted to the same fraction of valve diameter, find the increase in flow area. [29 %]

10 77. Why are exhaust valves smaller than the intake valves? Friction and Lubrication 78. A diesel engine is used in a truck requiring 80 kw. The mechanical efficiency of the engine is 80 %. The brake specific fuel consumption of the engine is 250 gm/kw-hr. A design improvement is made which reduces the engine friction by 3.7 kw. Assuming the indicated thermal efficiency remains the same, find (i) the new mechanical efficiency, (ii) the new bsfc, and (iii) the saving in fuel per hour. [83 %, gm/kw-hr, kg/hr] 79. A petrol engine with indicated thermal efficiency of 30 % has an fp of 18 kw at 1500 rpm and 45 kw at 2500 rpm. If the bp required at each speed is 75 kw and calorific value of the fuel is kj/kg, calculate the bsfc at both speeds, assuming indicated thermal efficiency to be same at both speeds. [0.337 kg/kw-hr, kg/kw-hr] 80. An eight cylinder engine when tested at a specified speed at 250 kg/hr air rate and 20 kg/hr fuel rate yields 63 kw. When the ignition to one of the cylinders is cut-off, the engine is found to deliver 52 kw. Assuming perfect distribution of air and fuel, estimate the fp of this engine under the stated conditions. [25 kw] 81. A five-cylinder, inline engine has an 8.15 cm bore, a 7.82 cm stroke, and connecting rod length of 15.4 cm. Each piston has a skirt length of 6.5 cm and a mass of 0.32 kg. At a certain engine speed and crank angle, the instantaneous piston speed is 8.25 m/s, and the clearance between the piston and cylinder wall is mm. SAE 10W-30 motor oil is used in the engine, and at the temperature of the piston-cylinder interface the dynamic viscosity of the oil is N-sec/m 2. Find the friction force on one piston at this condition. [ N] 82. A V6, two-stroke cycle SI automobile engine has a inch bore and 3.45 inch stroke. The pistons have a height of 2.95 inches and a diameter of 3.12 inches. At a certain point during the compression stroke, piston speed in one cylinder is ft/sec. The lubricating oil on the walls has a dynamic viscosity of lbf-sec/ft 2. Find the friction force on the piston under this condition. [20.76 lbf] 83. A four cylinder, two-stroke cycle engine, with a 2.65 litre displacement and crankcase compression, is running at 2400 rpm and at air-fuel ratio of 16.2:1. At this condition, the trapping efficiency is 72 %, relative charge is 87 %, and the exhaust residual from the previous cycle in each cylinder is 7 %. Oil is added to the intake air-flow such that the input fuel-to-oil ratio is 50:1. Calculate (a) rate of oil use, and (b) rate of unburnt oil added to the exhaust flow. [0.59 kg/hr, 0.17 kg/hr] 84. With reference to the forces acting on a piston, explain the terms (a) major thrust side and (b) minor thrust side. 85. State the desirable properties of lubricating oils. With reference to viscosity, how are the lubricating oils rated? Explain the meaning of SAE 15W-50.

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