6.1 SECTION 6 INTERNAL-COMBUSTION ENGINES Determining the Economics of Reciprocating I-C Engine Cogeneration 6.1 Diesel Generating Unit Efficiency 6.7 Engine Displacement, Mean Effective Pressure, and Efficiency 6.8 Engine Mean Effective Pressure and Horsepower 6.9 Selection of an Industrial Internal- Combustion Engine 6.10 Engine Output at High Temperatures and High Altitudes 6.11 Indicator Use on Internal-Combustion Engines 6.12 Engine Piston Speed, Torque, Displacement, and Compression Ratio 6.13 Internal-Combustion Engine Cooling- Water Requirements 6.14 Design of a Vent System for an Engine Room 6.18 Design of a Bypass Cooling System for an Engine 6.21 Hot-Water Heat-Recovery System Analysis 6.26 Diesel Fuel Storage Capacity and Cost 6.27 Power Input to Cooling-Water and Lube- Oil Pumps 6.29 Lube-Oil Cooler Selection and Oil Consumption 6.31 Quantity of Solids Entering an Internal- Combustion Engine 6.31 Internal-Combustion Engine Performance Factors 6.32 Volumetric Efficiency of Diesel Engines 6.34 Selecting Air-Cooled Engines for Industrial Applications 6.37 DETERMINING THE ECONOMICS OF RECIPROCATING I-C ENGINE COGENERATION Determine if an internal-combustion (I-C) engine cogeneration facility will be ec- onomically attractive if the required electrical power and steam services can be served by a cycle such as that in Fig. 1 and the specific load requirements are those shown in Fig. 2. Frequent startups and shutdowns are anticipated for this system. Calculation Procedure: 1. Determine the sources of waste heat available in the typical I-C engine There are three primary sources of waste heat available in the usual I-C engine. These are: (1) the exhaust gases from the engine cylinders; (2) the jacket cooling water; (3) the lubricating oil. Of these three sources, the quantity of heat available is, in descending order: exhaust gases; jacket cooling water; lube oil. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 6.2 POWER GENERATION FIGURE 1 Reciprocating-engine cogeneration system waste heat from the exhaust, and jacket a oil cooling, are recovered. (Indeck Energy Services, Inc.) FIGURE 2 Low-speed Diesel-engine cogeneration. (Indeck Energy Services, Inc.) 2. Show how to compute the heat recoverable from each source For the exhaust gases, use the relation, H A ϭ W(⌬t)(c g ), where W A ϭ rate of gas flow from the engine, lb /h (kg/h); ⌬t ϭ temperature drop of the gas between the heat exchanger inlet and outlet, ЊF(ЊC); c g ϭ specific heat of the gas, Btu /lb ЊF (J/kg ЊC). For example, if an I-C engine exhausts 100,000 lb/h (45,400 kg /h) at 700 ЊF (371ЊC) to a HRSG (heat-recovery steam generator), leaving the HRSG at 330 ЊF (166ЊC), and the specific heat of the gas is 0.24 Btu/lb ЊF (1.0 kJ/kg ЊC), Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES INTERNAL-COMBUSTION ENGINES 6.3 the heat recoverable, neglecting losses in the HRSG and connecting piping, is H A ϭ 100,000(700 Ϫ 330)(0.24) ϭ 8,880,000 Btu/h (2602 MW). With an average heat of vaporization of 1000 Btu/ lb (2330 kJ/ kg) of steam, this exhaust gas flow could generate 8,880,000 /1000 ϭ 8880 lb/ h (4032 kg/ h) of steam. If oil with a heating value of 145,000 Btu/ gal (40,455 kJ/L) were used to generate this steam, the quantity required would be 8,880,000 /145,000 ϭ 61.2 gal/h (232 L/h). At a cost of 90 cents per gallon, the saving would be $0.90(61.2) ϭ $55.08/h. Assuming 5000 hours of operation per year, or 57 percent load, the saving in fuel cost would be 5000($55.08) ϭ $275,400. This is a significant saving in any plant. And even if heat losses in the ductwork and heat-recovery boiler cut the savings in half, the new would still exceed one hundred thousand dollars a year. And as the operating time increases, so too do the savings. 3. Compute the savings potential in jacket-water and lube-oil heat recovery A similar relation can be used to compute jacket-water and lube-oil heat recovery. The flow rate can be expressed in either pounds (kg) per hour or gallons (L) per minute, depending on the designer’s choice. Since water has a specific heat of unity, the heat-recovery potential of the jacket water is H W ϭ w(⌬t w ), where w ϭ weight of water flow, lb per h (kg/h); ⌬t w ϭ change in temperature of the jacket water when flowing through the heat exchanger, ЊF(Њ C). Thus, if the jacket-water flow is 25,000 lb /h (11,350 kg/h) and the tem- perature change during flow of the jacket water through and external heat exchanger is 190 to 70 ЊF (88 to 21ЊC), the heat given up by the jacket water, neglecting losses is H w ϭ 25,000(190 Ϫ 70) ϭ 3,000,000 Btu/h (879 MW). During 25 h the heat recovery will be 24(3,000,000) ϭ 72,000,000 Btu (75,960 MJ). This is a significant amount of heat which can be used in process or space heating, or to drive an air- conditioning unit. If the jacket-water flow rate is expressed in gallons per minute instead of pounds per hour (L/min instead of kg/ h), the heat-recovery potential, H wg ϭ gpm(⌬t)(8.33) where 8.33 ϭ lb/gal of water. With a water flow rate of 50 gpm and the same temperature range as above, H wg ϭ 50(120)(8.33) ϭ 49,980 Btu/min (52,279 kJ / min). 4. Find the amount of heat recoverable from the lube oil During I-C engine operation, lube-oil temperature can reach high levels—in the 300 to 400 ЊF (149 to 201ЊC) range. And with oil having a typical specific heat of 0.5 Btu/lb ЊF (2.1 kJ /kg ЊC), the heat-recovery potential for the lube oil is ϭH w o w o (⌬t)(c o ), where w o ϭ oil flow in lb/ h (kg/h); ⌬t ϭ temperature change of the oil during flow through the heat-recovery heat exchanger ϭ oil inlet temperature Ϫ oil outlet temperature, ЊForЊC; c o ϭ specific heat of oil ϭ 0.5 Btu /lb ЊF (kJ/kg ЊC). With an oil flow of 2000 lb/ h (908 kg/h), a temperature change of 140 ЊF (77.7ЊC), H o ϭ 2000(140)(0.50) ϭ 140,000 Btu /h (41 kW). Thus, as mentioned earlier, the heat recoverable from the lube oil is usually the lowest of the three sources. With the heat flow rates computed here, an I-C engine cogeneration facility can be easily justified, especially where frequent startups and shutdowns are anticipated. Reciprocating Diesel engines are preferred over gas and steam turbines where fre- quent startups and shutdowns are required. Just the fuel savings anticipated for recovery of heat in the exhaust gases of this engine could pay for it in a relatively short time. Related Calculations. Cogeneration, in which I-C engines are finding greater use throughout the world every year, is defined by Michael P. Polsky, President, Indeck Energy Services, Inc., as ‘‘the simultaneous production of useful thermal Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES 6.4 POWER GENERATION energy and electric power from a fuel source or some variant thereof. It is more efficient to produce electric power and steam or hot water together than electric power alone, as utilities do, or thermal energy alone, which is common in industrial, commercial, and institutional plants.’’ Figures 1 and 2 in this procedure are from the firm of which Mr. Polsky is president. With the increased emphasis on reducing environmental pollution, conserving fuel use, and operating at lower overall cost, cogeneration—especially with Diesel engines—is finding wider acceptance throughout the world. Design engineers should consider cogeneration whenever there is a concurrent demand for electricity and heat. Such demand is probably most common in industry but is also met in commercial (hotels, apartment houses, stores) and institutional (hospital, prison, nursing-home) installations. Often, the economic decision is not over whether co- generation should be used, but what type of prime mover should be chosen. Three types of prime movers are usually considered for cogeneration—steam turbines, gas turbines, or internal-combustion engines. Steam and/or gas turbines are usually chosen for large-scale utility and industrial plants. For smaller plants the Diesel engine is probably the most popular choice today. Where natural gas is available, reciprocating internal-combustion engines are a favorite choice, especially with frequent startups and shutdowns. Recently, vertical modular steam engines have been introduced for use in co- generation. Modules can be grouped to increase the desired power output. These high-efficiency units promise to compete with I-C engines in the growing cogen- eration market. Guidelines used in estimating heat recovery from I-C engines, after all heat loses, include these: (1) Exhaust-gas heat recovery ϭ 28 percent of heat in fuel; (2) Jacket- water heat recovery ϭ 27 percent of heat in fuel; (3) Lube-oil heat recovery ϭ 9 percent of the heat in the fuel. The Diesel Engine Manufacturers Association (DEMA) gives these values for heat disposition in a Diesel engine at three-quarters to full load: (1) Fuel consumption ϭ 7366 Btu/bhp ⅐ h (2.89 kW /kW); (2) Useful work ϭ 2544 Btu/ bhp ⅐ h (0.999 kW/kW); (3) Loss in radiation, etc. ϭ 370 Btu / bhp ⅐ h (0.145 kW/ kW); (4) To cooling water ϭ 2195 Btu/ bhp ⅐ h (0.862 kW /kW); (5) To exhaust ϭ 2258 Btu/bhp ⅐ h (0.887 kW /kW). The sum of the losses is 1 Btu/bhp ⅐ h greater than the fuel consumption because of rounding of the values. Figure 3 shows a proposed cogeneration, desiccant-cooling, and thermal-storage integrated system for office buildings in the southern California area. While directed at the micro-climates in that area, similar advantages for other micro-climates and building types should be apparent. The data presented here for this system were prepared by The Meckler Group and are based on a thorough engineering and economic evaluation for the Southern California Gas Co. of the desiccant- cooling/thermal-energy-storage/ cogeneration system, a proprietary design devel- oped for pre- and post-Title-24 mid-rise office buildings. Title 24 is a section of the State of California Administrative Code that deals with energy-conservation standards for construction applicable to office buildings. A summary of the study was presented in Power magazine by Milton Meckler. In certain climates, office buildings are inviting targets for saving energy via evaporative chilling. When waste heat is plentiful, desiccant cooling and cogener- ation become attractive. In coupling the continuously available heat-rejection capacity of packaged cogeneration units, Fig. 4, with continuously operating re- generator demands, the use of integrated components for desiccant cooling, thermal- energy storage, and cogeneration increases. The combination also ensures a rea- sonable constant, cost-effective supply of essentially free electric power for general building use. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES INTERNAL-COMBUSTION ENGINES 6.5 FIGURE 3 Integrated system is a proposed off-peak desiccant/evaporative-cooling configu- ration with cogeneration capability. (Power and The Meckler Group.) Recoverable internal-combustion engine heat should at least match the heat re- quirement of the regenerator, Fig. 3. The selected engine size (see a later procedure in this section), however, should not cause the cogeneration system’s Purpa (Public Utility Regulatory & Policies Act) efficiency to drop below 42.5 percent. (Purpa efficiency decreases as engine size increases.) An engine size is selected to give the most economical performance and still have a Purpa efficiency of greater than 42.5 percent. The utility study indicated a favorable payout period and internal rate of return both for retrofits of pre-Title-24 office buildings and for new buildings in compli- ance with current Title-24 requirements (nominal 200 to 500 cooling tons). Al- though the study was limited to office-building occupancies, it is likely that other building types with high ventilation and electrical requirements would also offer attractive investment opportunities. Based on study findings, fuel savings ranged from 3300 to 7900 therms per year. Cost savings ranged from $322,000 to $370,000 for the five-story-building case studies and from $545,000 to $656,000 for 12-story-building case studies where the synchronously powered, packaged cogeneration unit was not used for emer- gency power. Where the cogeneration unit was also used for emergency power, the initial cost decreased from $257,000 to $243,000, representing a 31 percent drop in average cost for the five-story-building cases; and from $513,000 to $432,000, a 22 percent Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES 6.6 POWER GENERATION FIGURE 4 Packaged cogeneration I-C engine unit supplies waste heat to desiccant regenerator. (Power and The Meckler Group.) dip in average cost for the 12-story-building cases. The average cost decrease shifts the discounted payback period an average of 5.6 and 5.9 years for the five- and 12- story-building cases, respectively. Study findings were conservatively reported, since no credit was taken for po- tential income resulting from Purpa sales to the serving utility at off-peak hours, when actual building operating requirements fall below rated cogenerator output. This study is another example of the importance of the internal-combustion engine in cogeneration around the world today. Worldwide there is a movement toward making internal-combustion engines, and particularly diesel engines, cleaner-running. In general, this means reducing partic- ulate emissions from diesel-engine exhaust gases. For cities with large numbers of diesel-powered buses, exhaust emissions can be particularly unpleasant. And some medical personnel say that diesel exhaust gases can be harmful to the health of people breathing them. The approach to making diesel engines cleaner takes two tacts: (1) improving the design of the engine so that fewer particulates are emitted and (2) using cleaner fuel to reduce the particulate emissions. Manufacturers are using both approaches to comply with the demands of federal and state agencies regulating emissions. Today’s engineers will find that ‘‘cleaning up’’ diesel engines is a challenging and expensive procedure. However, cleaner-operating diesels are being introduced every year. *Elliott, Standard Handbook of Power Plant Engineering, McGraw-Hill, 1989. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES INTERNAL-COMBUSTION ENGINES 6.7 DIESEL GENERATING UNIT EFFICIENCY A 3000-kW diesel generating unit performs thus: fuel rate, 1.5 bbl (238.5 L) of 25 Њ API fuel for a 900-kWh output; mechanical efficiency, 82.0 percent; generator efficiency, 92.0 percent. Compute engine fuel rate, engine-generator fuel rate, in- dicated thermal efficiency, overall thermal efficiency, brake thermal efficiency. Calculation Procedure: 1. Compute the engine fuel rate The fuel rate of an engine driving a generator is the weight of fuel, lb, used to generate 1 kWh at the generator input shaft. Since this engine burns 1.5 bbl (238.5 L) of fuel for 900 kW at the generator terminals, the total fuel consumption is (1.5 bbl)(42 gal/bbl) ϭ 63 gal (238.5 L), at a generator efficiency of 92.0 percent. To determine the weight of this oil, compute its specific gravity s from s ϭ 141.5/(131.5 ϩ ЊAPI), where ЊAPI ϭ API gravity of the fuel. Hence, s ϭ 141.5(131.5 ϩ 25) ϭ 0.904. Since 1 gal (3.8 L) of water weighs 8.33 lb (3.8 kg) at 60 ЊF (15.6ЊC), 1 gal (3.8 L) of this oil weighs (0.904)(8.33) ϭ 7.529 lb (3.39 kg). The total weight of fuel used when burning 63 gal is (63 gal)(7.529 lb/gal) ϭ 474.5 lb (213.5 kg). The generator is 92 percent efficient. Hence, the engine actually delivers enough power to generate 900 /0.92 ϭ 977 kWh at the generator terminals. Thus, the engine fuel rate ϭ 474.5 lb fuel/ 977 kWh ϭ 0.485 lb /kWh (0.218 kg/ kWh). 2. Compute the engine-generator fuel rate The engine-generator fuel rate takes these two units into consideration and is the weight of fuel required to generate 1 kWh at the generator terminals. Using the fuel-consumption data from step 1 and the given output of 900 kW, we see that engine-generator fuel rate ϭ 474.5 lb fuel /900 kWh output ϭ 0.527 lb /kWh (0.237 kg/kWh). 3. Compute the indicated thermal efficiency Indicated thermal efficiency is the thermal efficiency based on the indicated horse- power of the engine. This is the horsepower developed in the engine cylinder. The engine fuel rate, computed in step 1, is the fuel consumed to produce the brake or shaft horsepower output, after friction losses are deducted. Since the mechanical efficiency of the engine is 82 percent, the fuel required to produce the indicated horsepower is 82 percent of that required for the brake horsepower, or (0.82)(0.485) ϭ 0.398 lb /kWh (0.179 kg/kWh). The indicated thermal efficiency of an internal-combustion engine driving a gen- erator is e i ϭ 3413/ƒ i (HHV), where e i ϭ indicated thermal efficiency, expressed as a decimal; ƒ i ϭ indicated fuel consumption, lb /kWh; HHV ϭ higher heating value of the fuel, Btu /lb. Compute the HHV for a diesel fuel from HHV ϭ 17,680 ϩ 60 ϫ ЊAPI. For this fuel, HHV ϭ 17,680 ϩ 60(25) ϭ 19,180 Btu/lb (44,612.7 kJ /kg). With the HHV known, compute the indicated thermal efficiency from e i ϭ 3,413/[(0.398)(19,180)] ϭ 0.447 or 44.7 percent. 4. Compute the overall thermal efficiency The overall thermal efficiency e o is computed from e o ϭ 3413/ƒ o (HHV), where ƒ o ϭ overall fuel consumption, Btu/kWh; other symbols as before. Using the Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES 6.8 POWER GENERATION engine-generator fuel rate from step 2, which represents the overall fuel consump- tion e o ϭ 3413/[(0.527)(19,180)] ϭ 0.347, or 34.7 percent. 5. Compute the brake thermal efficiency The engine fuel rate, step 1, corresponds to the brake fuel rate ƒ b . Compute the brake thermal efficiency from e b ϭ 3413/ƒ b (HHV), where ƒ b ϭ brake fuel rate, Btu/kWh; other symbols as before. For this engine-generator set, e b ϭ 3413/ [(0.485)(19,180)] ϭ 0.367, or 36.7 percent. Related Calculations. Where the fuel consumption is given or computed in terms of lb /(hp ⅐ h), substitute the value of 2545 Btu /(hp ⅐ h) (1.0 kW/kWh) in place of the value 3413 Btu /kWh (3600.7 kJ/kWh) in the numerator of the e i , e o , and e b equations. Compute the indicated, overall, and brake thermal efficiencies as before. Use the same procedure for gas and gasoline engines, except that the higher heating value of the gas or gasoline should be obtained from the supplier or by test. ENGINE DISPLACEMENT, MEAN EFFECTIVE PRESSURE, AND EFFICIENCY A12ϫ 18 in (30.5 ϫ 44.8 cm) four-cylinder four-stroke single-acting diesel engine is rated at 200 bhp (149.2 kW) at 260 r /min. Fuel consumption at rated load is 0.42 lb/(bhp ⅐ h) (0.25 kg /kWh). The higher heating value of the fuel is 18,920 Btu/lb (44,008 kJ/ kg). What are the brake mean effective pressure, engine dis- placement in ft 3 /(min ⅐ bhp), and brake thermal efficiency? Calculation Procedure: 1. Compute the brake mean effective pressure Compute the brake mean effective pressure (bmep) for an internal-combustion en- gine from bmep ϭ 33,000 bhp n /LAn, where bmep ϭ brake mean effective pressure, lb/in 2 ; bhp n ϭ brake horsepower output delivered per cylinder, hp; L ϭ piston stroke length, ft; a ϭ piston area, in 2 ; n ϭ cycles per minute per cylinder ϭ crank- shaft rpm for a two-stroke cycle engine, and 0.5 the crankshaft rpm for a four- stroke cycle engine. For this engine at its rated hbp, the output per cylinder is 200 bhp /4 cylinders ϭ 50 bhp (37.3 kW). Then bmep ϭ 33,000(50)/ [(18/12)(12) 2 ( /4)(260/2)] ϭ 74.8 lb/in 2 (516.1 kPa). (The factor 12 in the denominator converts the stroke length from inches to feet.) 2. Compute the engine displacement The total engine displacement V d ft 3 is given by V d ϭ LAnN, where A ϭ piston area, ft 2 ; N ϭ number of cylinders in the engine; other symbols as before. For this engine, V d ϭ (18/ 12)(12/12) 2 ( /4)(260/2)(4) ϭ 614 ft 3 /min (17.4 m 3 /min). The displacement is in cubic feet per minute because the crankshaft speed is in r/ min. The factor of 12 in the denominators converts the stroke and area to ft and ft 2 , respectively. The displacement per bhp ϭ (total displacement, ft 3 /min)/bhp output of engine ϭ 614/200 ϭ 3.07 ft 3 /(min ⅐ bhp) (0.12 m 3 /kW). 3. Compute the brake thermal efficiency The brake thermal efficiency e b of an internal-combustion engine is given by e b ϭ 2545/(sfc)(HHV), where sfc ϭ specific fuel consumption, lb/ (bhp ⅐ h); HHV ϭ Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES INTERNAL-COMBUSTION ENGINES 6.9 higher heating value of fuel, Btu/lb. For this engine, e b ϭ 2545 /[(0.42)(18,920)] ϭ 0.32, or 32.0 percent. Related Calculations. Use the same procedure for gas and gasoline engines. Obtain the higher heating value of the fuel from the supplier, a tabulation of fuel properties, or by test. ENGINE MEAN EFFECTIVE PRESSURE AND HORSEPOWER A 500-hp (373-kW) internal-combustion engine has a brake mean effective pressure of 80 lb /in 2 (551.5 kPa) at full load. What are the indicated mean effective pressure and friction mean effective pressure if the mechanical efficiency of the engine is 85 percent? What are the indicated horsepower and friction horsepower of the engine? Calculation Procedure: 1. Determine the indicated mean effective pressure Indicated mean effective pressure imep lb/in 2 for an internal-combustion engine is found from imep ϭ bmep /e m , where bmep ϭ brake mean effective pressure, lb / in 2 ; e m ϭ mechanical efficiency, percent, expressed as a decimal. For this engine, imep ϭ 80/0.85 ϭ 94.1 lb/in 2 (659.3 kPa). 2. Compute the friction mean effective pressure For an internal-combustion engine, the friction mean effective pressure ƒmep lb / in 2 is found from ƒmep ϭ imep Ϫ bmep,orƒmep ϭ 94.1 Ϫ 80 ϭ 14.1 lb/in 2 (97.3 kPa). 3. Compute the indicated horsepower of the engine For an internal-combustion engine, the mechanical efficiency e m ϭ bhp /ihp, where ihp ϭ indicated horsepower. Thus, ihp ϭ bhp /e m ,orihp ϭ 500 /0.85 ϭ 588 ihp (438.6 kW). 4. Compute the friction hp of the engine For an internal-combustion engine, the friction horsepower is ƒhp ϭ ihp Ϫ bhp.In this engine, ƒhp ϭ 588 Ϫ 500 ϭ 88 fhp (65.6 kW). Related Calculations. Use a similar procedure to determine the indicated en- gine efficiency e ei ϭ e i /e, where e ϭ ideal cycle efficiency; brake engine efficiency, e eb ϭ e b e; combined engine efficiency or overall engine thermal efficiency e eo ϭ e o ϭ e o e. Note that each of these three efficiencies is an engine efficiency and cor- responds to an actual thermal efficiency, e i , e b , and e o . Engine efficiency e e ϭ e t /e, where e t ϭ actual engine thermal efficiency. Where desired, the respective actual indicated brake, or overall, output can be substituted for e i , e b , and e o in the numerator of the above equations if the ideal output is substituted in the denominator. The result will be the respective engine efficiency. Output can be expressed in Btu per unit time, or horsepower. Also, e e ϭ actual mep/ ideal mep, and e ei ϭ imep /ideal mep; e eb ϭ bmep/ideal mep; e eo ϭ overall mep/ ideal mep. Further, e b ϭ e m e i , and bmep ϭ e m (imep). Where the actual heat supplied by the fuel, HHV Btu /lb, is known, compute e i e b and e o by the method given in the previous calculation procedure. The above relations apply to any re- ciprocating internal-combustion engine using any fuel. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES 6.10 POWER GENERATION TABLE 1 Internal-Combustion Engine Rating Table SELECTION OF AN INDUSTRIAL INTERNAL-COMBUSTION ENGINE Select an internal-combustion engine to drive a centrifugal pump handling 2000 gal/min (126.2 L/ s) of water at a total head of 350 ft (106.7 m). The pump speed will be 1750 r /min, and it will run continuously. The engine and pump are located at sea level. Calculation Procedure: 1. Compute the power input to the pump The power required to pump water is hp ϭ 8.33GH /33,000e, where G ϭ water flow, gal/min; H ϭ total head on the pump, ft of water; e ϭ pump efficiency, expressed as a decimal. Typical centrifugal pumps have operating efficiencies rang- ing from 50 to 80 percent, depending on the pump design and condition and liquid handled. Assume that this pump has an efficiency of 70 percent. Then hp ϭ 8.33(2000)/(350)/[(33,000)(0.70)] ϭ 252 hp (187.9 kW). Thus, the internal- combustion engine must develop at least 252 hp (187.9 kW) to drive this pump. 2. Select the internal-combustion engine Since the engine will run continuously, extreme care must be used in its selection. Refer to a tabulation of engine ratings, such as Table 1. This table shows that a diesel engine that delivers 275 continuous brake horsepower (205.2 kW) (the near- est tabulated rating equal to or greater than the required input) will be rated at 483 bhp (360.3 kW) at 1750 r/min. The gasoline-engine rating data in Table 1 show that for continuous full load at a given speed, 80 percent of the tabulated power can be used. Thus, at 1750 r/min, the engine must be rated at 252/0.80 ϭ 315 bhp (234.9 kW). A 450-hp (335.7- kW) unit is the only one shown in Table 1 that would meet the needs. This is too large; refer to another builder’s rating table to find an engine rated at 315 to 325 bhp (234.9 to 242.5 kW) at 1750 r/min. The unsuitable capacity range in the gasoline-engine section of Table 1 is a typical situation met in selecting equipment. More time is often spent in finding a Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2006 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTERNAL-COMBUSTION ENGINES