Problems of Practices Of Basic and Applied Thermodynamics I. C. Engine Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us brijrbedu@gmail.com. 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 cm 3. 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/cm 2 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/cm 2 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 Copyright by Brij Bhooshan @ 2013 Page 1
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 cm 3 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 15⁰ 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 cm 3 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/m 3 and density 0.592 kg/m 3 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/cm 2 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. Copyright by Brij Bhooshan @ 2013 Page 2
Problems of Practices on I. C. Engine By Brij Bhooshan 3 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 Stroke Brake dia Speed brake load 22 cm 27 cm 1.5 m 450 rev/min 4.6 kg imep 2.9 kgf/cm 2 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/m 3. 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 cm 2, 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. Copyright by Brij Bhooshan @ 2013 Page 3
4 Problems of Practices on I. C. Engine (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/m 3. (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). Copyright by Brij Bhooshan @ 2013 Page 4
Problems of Practices on I. C. Engine By Brij Bhooshan 5 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. Copyright by Brij Bhooshan @ 2013 Page 5
6 Problems of Practices on I. C. Engine 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/m 2 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/m 3. 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 m 3 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 Copyright by Brij Bhooshan @ 2013 Page 6
Problems of Practices on I. C. Engine By Brij Bhooshan 7 (ii) neglected; 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/m 3 and 750 kg/m 3 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 Copyright by Brij Bhooshan @ 2013 Page 7
8 Problems of Practices on I. C. Engine 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 mm 2 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% Copyright by Brij Bhooshan @ 2013 Page 8
Problems of Practices on I. C. Engine By Brij Bhooshan 9 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 Copyright by Brij Bhooshan @ 2013 Page 9
10 Problems of Practices on I. C. Engine 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 m 2 /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) < 10 9 Nu = 0.10 (Gr. Pr) 0.33 if (Gr. Pr) > 10 9. 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 141.5 P 131.5 API 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. Copyright by Brij Bhooshan @ 2013 Page 10
Problems of Practices on I. C. Engine By Brij Bhooshan 11 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 m 3, Calorific value of gas = 19000 kj/m 3, Density of gas = 1.275 kg/m 3, Air consumption = 32.1 m 3. Density of air = 1.29 kg/m 3, 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/m 3 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- Copyright by Brij Bhooshan @ 2013 Page 11
12 Problems of Practices on I. C. Engine 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 Copyright by Brij Bhooshan @ 2013 Page 12
Problems of Practices on I. C. Engine By Brij Bhooshan 13 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/m 3 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/8 th stroke 1.4 bar and at 7/8 th stroke 14 bar. Estimate the compression ratio. Calculate the air standard efficiency of the engine if the cut-off occurs at l/15 th 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/m 3 and 1.1122 kg/m 3 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 cm 3. 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 Copyright by Brij Bhooshan @ 2013 Page 13
14 Problems of Practices on I. C. Engine 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 PV 1.31 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/m 3. 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 Copyright by Brij Bhooshan @ 2013 Page 14
Problems of Practices on I. C. Engine By Brij Bhooshan 15 (i) (ii) Time for one injection. 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 Copyright by Brij Bhooshan @ 2013 Page 15
16 Problems of Practices on I. C. Engine 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/cm 2 and 30 C which is compressed to 15 kg/cm 2 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/cm 2 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/cm 2. Also calculate the work done and heat transferred during the process, indicating the direction of Copyright by Brij Bhooshan @ 2013 Page 16
Problems of Practices on I. C. Engine By Brij Bhooshan 17 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 cm 2 ; 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/cm 2, (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/cm 2 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 p V 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/m 2 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: Copyright by Brij Bhooshan @ 2013 Page 17
18 Problems of Practices on I. C. Engine 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 Copyright by Brij Bhooshan @ 2013 Page 18
Problems of Practices on I. C. Engine By Brij Bhooshan 19 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 cm 3 /cycle/cylinder in terms of injection pressure pinj (kn/m 2 ), combustion chamber pressure pcyl (kn/m 2 ), density of fuel pf(kg/cm 3 ) 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 m 3 of free air Copyright by Brij Bhooshan @ 2013 Page 19