Tài liệu Handbook of Mechanical Engineering Calculations P9 pdf

9.1 SECTION 9 AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS Estimating the Cost of Air Leaks in Compressed-Air Systems 9.1 Selecting an Air Motor for a Known Application 9.4 Air-Compressor Cooling-System Choice for Maximum Coolant Economy 9.10 Economics of Air-Compressor Inlet Location 9.14 Power Input Required by Centrifugal Compressor 9.16 Compressor Selection for Compressed- Air Systems 9.18 Sizing Compressed-Air System Components 9.24 Compressed-Air Receiver Size and Pump-Up Time 9.26 Vacuum-System Pump-Down Time 9.27 Vacuum-Pump Selection for High- Vacuum Systems 9.30 Vacuum-System Pumping Speed and Pipe Size 9.33 Determining Air Leakage in Vacuum Systems by Calculation 9.34 Checking the Vacuum Rating of a Storage Vessel 9.36 Sizing Rupture Disks for Gases and Liquids 9.39 Determining Airflow in Pipes, Valves, and Fittings 9.40 System Economics and Design Strategies ESTIMATING THE COST OF AIR LEAKS IN COMPRESSED-AIR SYSTEMS Find the cost of compressed air leaking through a 0.125-in (0.3175-cm) diameter hole in a pipe main of a typical industrial air piping system, Fig. 1, to the atmo- sphere at sea level when the air pressure in the pipe is 10 lb/in 2 (gage) (68.9 kPa), the plant, Fig. 2, operates 7500 h/yr, air temperature is 70 Њ F (21.1 Њ C), and the cost of compressed air is $1.25 per 1000 ft 3 (28.3 m 3 ). What is the cost of the leaking air when the pipe pressure is 50 lb/in 2 (gage) (344.5 kPa) and the other variables are the same as given above? Calculation Procedure: 1. Find the volume of air discharged to the atmosphere Air flowing through an orifice or nozzle attains a critical pressure of 0.53 times the inlet or initial pressure. This reduced pressure occurs at the throat or vena contracta, which is the point of minimum stream diameter on the outlet side of the air flow. If the outlet or back pressure exceeds the critical pressure then the vena contracta 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 9.2 PLANT AND FACILITIES ENGINEERING FIGURE 1 Typical compressed-air system main and branch pipes (Factory Manage- ment and Maintenance). or throat pressure rises to equal the backpressure. Air flow through a hole in a pipe or tank replicates the flow through an orifice or nozzle. When an inlet air pressure of 10 lb/ in 2 (gage) ϩ 14.7 ϭ 24.7 lb/in 2 (abs) (170.2 kPa), the critical pressure is 0.53 ϫ 24.7 ϭ 13.09 lb/ in 2 (abs) (90.2 kPa). Since 13.09 lb /in 2 (abs) is less than the atmospheric backpressure of 14.7 lb/ in 2 (abs) (101.3 kPa), the throat pressure equals the backpressure, or 14.7 lb/in 2 (abs) (101.3 kPa). Knowing this, we can compute weight of the escaping air from W ϭ 1.06 A(P 1 [P Ϫ P 1 ]/T) 0.5 , where W ϭ leakage rate, lb /s (kg /s); A ϭ area of leakage hole, in 2 (cm 2 ); P ϭ pipeline or initial air pressure, lb/ in 2 (abs) (kPa); P 1 ϭ outlet or backpressure, lb/ in 2 (abs); T ϭ absolute temperature of the air before leakage ϭ Њ F ϩ 460. Substituting, using the values given above, W ϭ 1.06 ϫ 0.012272(14.7[24.7 Ϫ 14.7]/ 530) 0.5 ϭ 0.006851 lb/s (0.0031 kg/ s). Converting this air leakage rate to lb/ h (kg/h), multiply by 3600 s/h, or 0.006851 ϫ 3600 ϭ 24.66 lb/ h (11.19 kg/ h). Since the cost of compressed air is expressed in $/ft 3 , the flow rate of the leaking air must be converted. Since air at 14.7 lb/in 2 (abs) (101.3 kPa) weighs 0.075 lb per ft 3 (1.2 kg/ m 3 ), the rate of leakage is 24.66/0.075 ϭ 328.8 ft 3 /h (9.31 m 3 /h). 2. Determine the annual cost of the air leakage This compressed-air plant operates 7500 h/ yr. Since the leakage rate is 328.8 ft 3 /h, the annual leakage through this opening is 7500 ϫ 328.8 ϭ 2,466,000 ft 3 (58,691 m 3 ). At a cost of $1.25 per 1000 ft 3 , the annual total cost of this leak is $1.25 ϫ 2,466,000/ 1000 ϭ $3,082.50. This is a sizeable charge, especially if there are several leaks of this size, or larger, in the system. 3. Find the rate of leakage at the higher line pressure When the backpressure is less than the critical pressure, a different flow equation must be used. In the second instance, the critical pressure is 0.53 (50 lb/in 2 (gage) ϩ 14.7) ϭ 34.29 lb /in 2 (abs) (236.26 kPa). Since 34.29 lb/in 2 (abs) (236.26 kPa) is greater than the atmospheric backpressure of 14.7 lb/ in 2 (abs) (101.3 kPa), the critical pressure is greater than the backpressure. Air leakage through the hole is now given by W ϭ 0.5303(ACP)/(T) 0.5 , where C ϭ flow coefficient ϭ 1.0; other symbols as before. 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.3 FIGURE 2 Typical compressed-air plant showing compressor and its associated piping and accessories (Power). 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.4 PLANT AND FACILITIES ENGINEERING Substituting, W ϭ 0.5303(0.012272)(1.0)(64.7)/ (530) 0.5 ϭ 0.01829 lb /s (0.0083 kg/ s). Converting to an hourly flow rate as earlier, 3600 ϫ 0.01828 ϭ 65.84 lb/ h (29.89 kg/ h). 4. Compute the annual cost of air leakage at the higher pressure Following the same steps as earlier, annual leakage cost ϭ 65.84 lb /h (7500 h/ yr)(1.25/ 1000 ft 3 )/ 0.075 lb /ft 3 ϭ $8,230.00 per year. Again, this is a significant loss of revenue. Further, the loss at the higher pressure is $8230 /3082.50 ϭ 2.67 times as great. This points out the fact that higher pressures in a compressed-air system can cause more expensive leaks. Related Calculations. Compressing air requires a power input to raise the air pressure from atmospheric to the level desired for the end use of the air. When compressed air leaks from a pipe or storage tank, the power expended in compres- sion is wasted because the air does no useful work when it leaks into the atmo- sphere. In today’s environment-conscious world, compressed-air leaks are considered to be especially wasteful because they increase pollution without producing any ben- eficial results. The reason for this is that the fuel burned to generate the power to compress the wasted air pollutes the atmosphere unnecessarily because the air pro- duces only a hissing sound as it escapes through the hole in the pipe or vessel. SELECTING AN AIR MOTOR FOR A KNOWN APPLICATION Show how to select a suitable air motor for a reversible application requiring 2 hp (1.5 kW) at 1000 rpm for an industrial crane. Determine the probable weight of the motor, its torque output, and air consumption for this intermittent duty appli- cation. An adequate supply of air at a wide pressure range is available at the installation. Calculation Procedure: 1. Assemble data on possible choices for the air motor There are four basic types of air motors in use today: (1) radial-piston type; (2) axial-piston type; (3) multi-vaned type; (4) turbine type. Each type of air motor has advantages and disadvantages for various applications. Characteristics of these air motors are as follows: (1) Radial-piston air motors, Fig. 3, have four or five cylinders mounted around a central crankshaft similar to a radial gasoline engine. Five cylinders are preferred to supply more horsepower with evenly distributed power pulses. In such a unit there are always two cylinders having a power stroke at the same time. The radial- piston motor is usually a slow-speed unit, ranging from 85 to 1500 rpm. It is suited for heavy-duty service up to 20 hp (15 kW) where good lugging characteristics are needed. Normally they are not reversible, though reversible models are available at extra cost. (2) Axial-piston air motors, Fig. 4, are more compact in design and require less space than a four- or five-cylinder radial-piston motor. Air drives the pistons in translation; a diaphragm-type converter changes the translation into rotation. This arrangement supplies high horsepower per unit weight. Axial-piston motors are 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.5 FIGURE 3 (a) Five-cylinder piston-type radial air motor used in sizes from about 2 hp (1.5 kW) to 22 hp (16.4 kW) and at speeds from 85 to 1500 rpm. (b) How five-cylinder air motor distributes power. Two cylinders are always on power stroke at any instant (Gardner-Denver Company). available in sizes from 0.5 to 2.75 hp (0.37 to 2.1 kW). They run equally well in either direction. To make the motor reversible, a four-way air valve is inserted in the line. (3) Multi-vaned motors, Fig. 5, are suitable for loads from fractional hp (kW) to 10 hp (7.5 kW). They are relatively high-speed units which must be geared down for usable speeds. The major advantages of multi-vaned motors is light weight and small size. However, if used at slow speed, the gearing may add significantly to the weight of the motor. (4) Air-turbine motors deliver fractional horsepowers at exceptionally high speeds, from 10,000 to 150,000 rpm, and are an economical source of power. They are tiny impulse-reaction turbines in which air at 100 psi (689 kPa) impinges on buckets for the driving force. Force-feed automatic lubrication sprays a fine film of oil on to bearings continuously, minimizing maintenance. Based on the load requirements, 2 hp (1.5 kW) at 1000 rpm, a reversible radial- piston air motor, Table 1, would be a suitable choice because it delivers up to 2.8 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.6 PLANT AND FACILITIES ENGINEERING Diaphragm converts piston translation to rotation Pistons (four or five) Output shaft FIGURE 4 Axial-piston air motor available in various output sizes (Keller Tool Com- pany). FIGURE 5 Typical multi-vane type air motor, available in fractional hp sizes and up to some 10 hp (7.5 kW) (Gast Manufacturing Company). 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.7 TABLE 1 Specifications of Typical Air Motors Rated hp* (kW) Speed at rated hp—rpm Free speed rpm Weight lb (kg) Stall torque ft—lbs Air consumption at rated hp ft 3 free air/min Radial piston motors (non-reversible)* 2.9 (2.2) 1,500 3,200 130 (59) 3.3 (2.5) 1,300 3.000 130 (59) 3.8 (2.8) 1,200 2,700 130 (59) Radial piston motors (reversible)* 2.5 (1.7) 1,200 2,200 135 (61.3) 2.8 (2.1) 1,000 1,950 135 (61.3) 3.2 (2.4) 900 1,600 135 (61.3) 5.2 (3.9) 750 1,600 200 (90.8) *at 90 lb / in 2 (620 kPa). Ingersoll-Rand. hp (2.1 kW) at 1000 rpm with air delivered to the motor at 90 lb/ in 2 (620 kPa). The weight of this motor, Table 1, is 135 lb (61.3 kg). 2. Compare the advantages of air motors to other types of motive power Air motors have a number of advantages over their usual competitors—electric motors. These advantages are: (1) In explosive or gaseous environments, air motors are lower in cost than larger, heavier, explosion-proof electric motors. Air motors operate relatively trouble-free in moist, humid environments where the electric mo- tor may suffer from a buildup of fungus and corrosion. And since the air motor requires little maintenance, it can be mounted in inaccessible locations. (2) With an air motor, the output speed can be varied from zero to free-speed no-load rotation by merely changing the volume of air supplied to the motor. Controls are simple in design and use. (3) Air motors can weigh as little as one-quarter that of electri- cally-powered units; their physical dimensions are about 50 percent those of elec- trical devices. Further, air motors do not spark; they cannot burn out from over- loading; the air motor is not injured by stalling. Air motors start and stop positively; they have a consistent output torque which can be changed by varying the inlet air pressure. Air motors do, however, have limitations. Thus: (1) Compared to electric motors, air motors are inefficient. An air motor requires about 5 hp (3.7 kW) input to the air compressor to produce one horsepower (0.7 5kW) at the motor outlet. (2) Air motors are rarely practical in sizes greater than 20 hp (15 kW). Their most efficient range is 1 /20 to 20 hp (0.04 to 15 kW). (3) The initial cost of an air motor is high; in larger sizes, above 1 hp (0.75 kW), air motors cost up to five times that of equivalent electric motors. 3. Check the motor duty cycle and load against the unit’s characteristics When selecting an air motor, the first factor to be considered is the type of duty cycle, intermittent or continuous. A crane, for which this motor will be used, does have an intermittent duty cycle because it is not normally used continuously. There is a rest period while the crane load is being put on the crane and again while being off-loaded from the crane. The great majority of air-motor applications have a low-load cycle; the air mo- tors are used for only a few seconds continuously and have long off-duty periods. 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.8 PLANT AND FACILITIES ENGINEERING Torque Horsepower Governor controlled curves Rated performance Horsepower Torque Speed RPM 1 Free speed 0 Stall speed FIGURE 6 Performance curve of a typical air motor. Note how a built-in governor can change the shape of the curve by limiting the maximum speed of the air motor (Product Engineering). The duty cycle will usually determine the type of motor and the size of compressor that must be used. 4. Check the horsepower and speed required Performance curves, Fig. 6, show an air motor’s torque and horsepower (kW) output at various rpm. Such curves can be varied somewhat by using governors or by modifying the air intake or exhaust ports. However, the basic shape of the perform- ance curve depends on the fundamental design of the air motor. It is common practice to rate an air motor at its maximum output, i.e., at the top of the dome- shaped performance curve. The reversible radial-piston motor chosen here has ad- equate horsepower and speed for the anticipated load. 5. Determine the effect of air pressure and quantity on the air motor output Table 2 shows how the air pressure available at the motor inlet affects both the power output and rpm of typical air motors. For the motor being considered here, the output would be sufficient at the lowest air pressure listed. Thus, the motor choice is acceptable. 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.9 TABLE 2 Effect of Air Pressure on Motor Performance Motor style no. Rated hp (kW) 1234 5 rpm at rated hp 1 2 345 Free speed—rpm 12345 At 60 psi lb /in 2 1.9 2.5 3.2 6.4 0.4 1,200 1,100 850 800 900 2,650 2,250 2,030 1,900 1,600 (413 kPa) (1.4) (1.9) (2.4) (4.8) (0.29) Gardner-Denver Company. 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.10 PLANT AND FACILITIES ENGINEERING Related Calculations. When using tables of air-motor performance, it is im- portant to keep in mind that the stall torque and air consumption vary for each motor. Hence, these values are not listed in the usual performance tables. There are so many variables in air-motor choice that stall torque and air consumption are unique for each application and are supplied by the motor manufacturer when the motor choice is made. As a general rule of thumb, stall torque ranges between 2 and 2.5 times the torque developed when operating at maximum horsepower output. In small motors, up to 2.5 hp (1.9 kW), air consumption varies from 35 to 40 ft 3 /min (0.99 to 1.1 m 3 /min) of free air per hp (0.746 kW). Larger air motors consume 20 to 25 ft 3 /min (0.57 to 0.70 m 3 /min) of free air per hp. These con- sumption rates apply to non-reversible motors. Reversible air motors consume 30 to 35 percent more air. The data, tables and illustration in this procedure are from Product Engineering magazine. AIR-COMPRESSOR COOLING-SYSTEM CHOICE FOR MAXIMUM COOLANT ECONOMY Select a suitable cooling system for a two-stage 5000-hp (3730-kW) engine-driven air compressor, Fig. 7, installed in a known arid hard-water area when the rated output of the compressor is 25,000 ft 3 /min (708 m 3 /min) at 100 lb/ in 2 (abs) (689 kPa). Water conservation is an important requirement for this compressor because of the arid nature of the area in which the unit is installed. Use standard cooling- water requirements in estimating the capacity of the cooling system. Calculation Procedure: 1. Assess the types of cooling systems that might be used Several types of cooling systems can be used for air compressors such as this. Because the air compressor is used in an arid area subject to water shortages, a recirculating system of some type is immediately indicated. Since both the engine and air-compressor cooling water require temperature reduction in such an instal- lation, the two requirements are usually combined in one cooling system. The first arrangement that might be chosen, Fig. 8, combines a heat exchanger for engine power-cylinder cooling and a cooling tower for raw-water cooling for the compressor. Either a natural-draft cooling tower, such as that shown, or a me- chanical-draft cooling tower might be used. The cooling-tower choice depends on a number of factors. In an arid area, however, natural-draft towers are known to perform well in dry climates. Further, they require much less piping and electric wiring than mechanical-draft towers. Another possible cooling-system arrangement uses a closed coil in the cooling tower for both the power and air cylinders, Fig. 9. This totally closed system does not allow contact between the compressor and engine cooling water with the at- mosphere. This means that the compressor and engine cooling water can be treated to reduce scale formation. Raw water recirculated through the cooling tower does not contact the compressor coolant. Where installation costs are critical, raw water can be used to cool the air- compressor cylinders, Fig. 10. The engine power cylinders, which usually operate 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. AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS [...]... because of the possibility of scale and impurities buildup (Ingersoll-Rand Co.) 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 AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.14 PLANT AND FACILITIES ENGINEERING higher flow rate of 2.8... displacement of an air compressor is the volume of air displaced per unit of time, usually stated in ft3 / min In a multistage compressor, the displacement is that of the low-pressure cylinder only 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... 2.91 in (7.4 cm) Related Calculations The air consumption of power tools is normally expressed in ft3 / min of free air at sea level; the actual capacity of any type of air compressor is expressed in the same units At locations above sea level, the quantity of free air required to operate an air tool increases because the atmospheric pressure is lower To find the air consumption of an air tool at an altitude... 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 AIR AND GAS COMPRESSORS AND VACUUM SYSTEMS 9.28 PLANT AND FACILITIES ENGINEERING TABLE 9 Evacuation Time Calculations Enter in the second column of Table 9 the ratio of the absolute pressure... from a minimum of about 1 hp (0.7 kW) to a maximum of about 3 hp (2.2 kW) If another pump could evacuate this receiver in 6 min and needed only 2.5 hp (1.9 kW) as the maximum power input, it might be a better choice, provided that its first cost were not several times that of the other pump Use the methods of engineering economics to compare the economic merits of the two pumps Related Calculations Note... cases where operational methods cannot be used, empirical calculations may be convenient Although not as rigorous, empirical methods yield reasonable values for a first approach in engineering calculations The Heat Exchange Institute (Cleveland OH) publishes a set of air leakage curves for empirical calculations, as a function of the volume of the system and the operational pressure Such curves give... intake volume, I, required to deliver 1000 ft3 / min of free air at each of the possible intake temperatures from I ϭ 1000(density of air at 70 ЊF, lb / ft3 / 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 AIR AND GAS COMPRESSORS... plants of all types—chemical, petroleum, manufacturing, marine, industrial, etc This procedure has universal application because it is based on the properties of air, the compressor power input, the annual operating hours, and the cost of power These values can be found in any application of air compressors in industry today Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)... terms of ft3 / min of free air at the elevation location, multiply the sea-level consumption by the appropriate factor from Table 6 Thus, a tool that consumes 10 ft3 / min (0.005 m3 / s) of free air at sea level will use 10 (1.310) ϭ 13.1 ft3 / min (0.006 m3 / s) of 100 lb / in2 (689.5-kPa) free air at an 8000-ft (2438.4-m) altitude Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)... compressor handling air draws in 12,000 ft3 / min (339.6 m3 / min) of air at a pressure of 14 lb / in2 (abs) (96.46 kPa) and a temperature of 60ЊF (15.6ЊC) 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 AIR AND GAS COMPRESSORS AND VACUUM . subject to the Terms of Use as given at the website. Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS 9.2 PLANT AND FACILITIES ENGINEERING FIGURE. weight of this motor, Table 1, is 135 lb (61.3 kg). 2. Compare the advantages of air motors to other types of motive power Air motors have a number of advantages