Thumb for Mechanical Engineers 2011 Part 5 docx

110 Rules of Thumb for Mechanical Engineers COMPRESSORS* The following data are for use in the approximation of horsepower needed for compression of gas. Definitlons The “N value” of gas is the ratio of the specific heat at constant pressure (CJ to the specific heat at constant vol- ume (G). If the composition of gas is known, the value of N for a gas mixture may be determined from the molal heat capac- ities of the components. If only the specific gravity of gas is known an approximate N value may be obtained by using Piston Displacement of a compressor cylinder is the vol- ume swept by the piston with the proper deduction for the piston rod. The displacement is usually expressed in cubic ft per minute. Clearance is the volume remaining in one end of a cylin- der with the piston positioned at the end of the delivery stroke for this end. The clearance volume is expressed as a percentage of the volume swept by the piston in making its the chart in Figure 1. full delivery stroke for the end of the cylinder being consid- ered. Ratio of comprespion is the ratio of the absolute dis- charge pressure to the absolute inlet pressure. Actual capacity is the quantity of gas compressed and delivered, expressed in cubic ft per minute, at the intake pressure and temperature. Volumetric efficiemy is the ratio of actual capacity, in cubic ft per minute, to the piston displacement, in cubic ft per minute, expressed in percent. Adiabatic horsepower is the theoretical horsepower re- quired to compress gas in a cycle in which there is no trans- fer of sensible heat to or from the gas during compression or expansion. Isothermal horsepower is the theoretical horsepower re quid to compress gas in a cycle in which there is no change in gas temperature during compression or expan- sion. Indicated horsepower is the actual horsepower required to compress gas, taking into account losses within the com- pressor cylinder, but not taking into account any lm in frame, gear or power transmission equipment. 0 Figure 1. Ratio of specific heat (n-value). *Reprinted from Pipe Line Rules of Thumb Handbook, 3rd Ed., E. W. McAllister (Ed.), Gulf Publishing Company. Houston, Texas, 1993. Pumps and Compressors 11 1 Compression efficiency is the ratio of the theoretical horsepower to the actual indicated hompower, required to compress a definite amount of gas. The efficiency, ex- pressed in percent, should be defined in regard to the base at which the themetical power was calculated, whether adiabatic or isothermal. Mechanid efficiency is the ratio of the indicated horse power of the compressor cylinder to the brake horsepawer delivered to the shaft in the case of a power driven ma- overall e&ciency is the product, expressed in percent, of the compression efficiency and the mechanical efficiency. It must be defined according to the base, adiabatic isother- chine. rt is expressed in percent. mal, which was used in establishing the compression &i- ciency. Piston rod gas load is the varying, and usually revensing, load imposed on the piston rod and crosshead during the operation, by Werent gas pressures existing on the faces of the compressor piston. The maximum piston rod gas load is determined for each compressor by the manufacturer, to limit the stresses in the frame members and the bearing loads in accordance with mechanical design. The maximum allowed piston rod gas load is affecbd by the ratio of compression and also by the cylinder design; i.e., whether it is single or double acting. ~ Performance Calculations for Reciprocating Compressors Piston Dlsplacement & L = 0.3 for lubricated compresors Let L = 0.07 for mn lubricated compressors (6) Single acting compressor: These values are approximations and the exact value may vary by as much as an additional 0.02 to 0.03. Note: A value of 0.97 is used in the volumetric efficiency equation rather than 1.0 since even with 0 clearance, the cylinder will not fill perfectly Pd = [& X N X 3.1416 X D2]/[4 X 1,7281 (1) Double acting compressor without a tail rod: Pd = [& X N X 3.1416 X (m2 - d2)]/[4 X 1,7281 (2) Double acting compressor with a tail rod: Cylinder Inlet capadty Pa = [S, x N x 3.1416 x 2 x (D* - d*)]/[4 x 1,7281 (3) Q1 = E, Single acting compressor compressing on frame end Piston Speed only: Pa [S, x N x 3.1416 x @B - d*)]/[4 x 1,7281 PS = [2 x S, x N]/12 (4) Dlscharge Temperature where Pd = Cylinder displacement, cu Wmin T2 = T1(rP@-')9 S, = Stroke length, in. N = Compressor speed, number of compression strokedmin D = Cylinder diameter, in. d = Piston rod diameter, in. Volumetric Efficiency where Te = Absolute discharge temperature OR T1 = Absolute suction temperature OR Note: Even though this is an adiabatic relationship, cyl- inder cooling will generally offset the effect of efficiency. Power E, = 0.97 - [(l/f)rPlk - 1]C - L (5) where & = Volumetric efficiency f = ratio of discharge compressibility to suction Wqi 1144 PiQd33,~ %1l x W& - U1 x [r:-Uk - 11 (10) ~Ssibility -1 rp = pressure ratio k = isentropic exponent L = gas slippage factor C = percent clearance where %l=efficiency Wvi Cylinda horsepower 112 Rules of Thumb for Mechanical Engineers See Figure 2 “Reciprocating compressor eff1ciencies”for curve of efficiency vs pressure ratio. This curve includes a 95% mechanical efficiency and a valve velocity of 3,000 ft. per minute. Tables 1 and 2 permit a correction to be made to the com- pressor horsepower for specific gravity and low inlet pressure. While it is recognized that the efficiency is not necessarily the element affected, the desire is to modify the power required per the criteria in these figures. The efficiency correction accom- om son sen 87n sn 35s 841 83s am sin 791 77n a01 781 76n 7H 7I 73s 7m 71U 701 1.5 2 2.5 I 3.5 4 4.5 5 5.5 6 SA rRLsSURr RATIO Reciprocating compressor efficiencies plotted against pressure ra- tio with a valve velocity of 3,000 fpm and a mechanical efficiency of 95 percent. Figure 2. Reciprocating compressor efficiencies. I M 03 ad u U ID Wulllnatm 0 marm x POlyRT Figure 3. Volume bottle sizing. plishes this. These corrections become more significant at the lower pressure ratios. Inlet Valve Velocity where V = Inlet valve velocity A = Product of actual lift and the valve opening periphery and is the total for inlet valves in a cylinder expressed in square in. (This is a com- pressor vendor furnished number.) Example. Calculate the following: Suction capacity Horsepower Discharge temperature Piston speed Given: Bore = 6 in. Stroke = 12 in. Speed = 300 rpm Rod diameter = 2.5 in. Clearance = 12% Gas = COZ Inlet pressure = 1,720 psia Discharge pressure = 3,440 psia Inlet temperature = 115°F Calculate piston displacement using Equation 2. Pd = 12 x 300 x 3.1416 x [2(6)’ - (2.5)’]/1,728 x 4 = 107.6 cfm Calculate volumetric efficiency using Equation 5. It will first be necessary to calculate f, which is the ratio of dis- charge compressibility to suction compressibility. TI = 115 + 460 = 575”R T, = TIT, = 5751548 = 1.05 where T, = Reduced temperature T, = Critical temperature = 548” for COZ T = Inlet temperature P, = PIP, = 1,72011,071 = 1.61 Pumps and Compressors 113 r, 3.0 1.5 2.0 1.5 where P, = Redd pressure Calculate suction capacity. P, = Critical pressure = 1,071 psia for CO, P = suction presrmre QI = Ev X pd = 0.93 x 107.6 = 100.1 cfm From the generalized compressibility chart (Figure 4): k SunPah 10 14.7 20 40 80 a0 100 150 .990 1.00 1.00 1.00 1.00 1.00 1.00 1.00 .980 ,985 ,990 ,995 1.00 1.00 1.00 1.00 .980 .a65 370 .geO .WO 1.09 1.00 1.00 .890 .900 -820 -940 .o(M -980 .SSO 1.00 Z1 0.312 Calculate piston speed. PS = [2 x S, x N]/12 = [2 x 12 x 300]/12 = 600 Wmin Determine discharge compressibility. Calculate dis- charge temperature by using Equation 9. E, = 0.97 - [(1/1.843) x 2.01'1-3 - 11 X 0.12 - 0.05 = 0.929 = 93% Note: A value of 0.05 was used for L because of the high rp = 3,4Ao11,720 =2 ~ SO rr 1s 1.3 1.0 os 0.8 2.0 am ID 1.0 1.0 1.01 ~~ 1.75 0.87 os 1.0 1.01 1.m 1.6 as4 0.w 1.0 1.02 1.04 k = q/cv = 1.3 for Cog TI = 674.71548 = 1.23 PI = 3,44011,071 = 3.21 From the generalized cnmpressibilty chart (Figure 4): Z, = 0.575 f = 0.57511.61 = 1.843 Table 2 Efflclency Multiplier for Speclflc Gravlty 114 Rules of Thumb for Mechanical Engineers Figure 4. Compressibility chart for low to high values of reduced pressure. Reproduced by permission of Chemical Engineering, McGraw Hill Publications Company, July 1954. Estimating suction and discharge volume bottle sizes for pulsation control for reciprocating compressors Pressure surges are created as a result of the cessation of flow at the end of the compressor’s discharge and suction stroke. As long as the compressor speed is constant, the pressure pulses will also be constant. A low pressure com- pressor will likely require little if any treatment for pulsa- tion control; however, the same machine with increased gas density, pressure, or other operational changes may de- velop a problem with pressure pulses. Dealing with pulsa- tion becomes more complex when multiple cylinders are connected to one header or when multiple stages are used. API Standard 618 should be reviewed in detail when planning a compressor installation. The pulsation level at the outlet side of any pulsation control device, regardless of type, should be no more than 2 % peak-to-peak of the line pressure of the value given by the following equation, whichever is less. Pumps and Compressors 115 Where a detailed pulsation analysis is required, several approaches may be followed. An analog analysis may be performed on the Southern Gas Association dynamic com- pressor simulator, or the analysis may be made a part of the compressor purchase contract. Regardless of who makes the analysis, a detailed drawing of the piping in the com- pressor area will be needed. The following equations are intended as an aid in esti- mating bottle sizes or for checking sizes proposed by a ven- dor for simple installations-i.e., single cylinder connected to a header without the interaction of multiple cylinders. The bottle type is the simple unbaffled type. (12) Calculate discharge volumetric efficiency using Equa- tion 13: Example. Determine the approximate size of suction and discharge volume bottles for a single-stage, singleact- ing, lubricated compressor in natural gas service. Cylinder bore = 9 in. Cylinder stroke = 5 in. Rod diameter = 2.25 in, Suction temp = 80'F Discharge temp = 141'F Suction pressure = 514 psia Discharge pressure = 831 psia Isentropic exponent, k = 1.28 Specific gravity = 0.6 Percent clearance = 25.7% Step 1. Determine suction and discharge volumetric effi- ciencies using Equations 5 and 13. rp = 831/514 = 1.617 Z1= 0.93 (from Figure 5) Z, = 0.93 (from Figure 5) f = 0.93/0.93 = 1.0 Calculate suction volumetric efficiency using Equation 5: & = 1 x [0.823]/[1.6171/'.e8] = 0.565 Calculate volume displaced per revolution using Equa- tion l: PdlN S, x 3.1416 X De/[1,728 x 41 = [5 x 3.1416 x 9']/[1,728 x 41 = 0.184 cu ft or 318 cu in. Refer to Figure 3, volume bottle sizing, using volumetric efficiencies previously calculated, and determine the multi- pliers. Suction multiplier = 13.5 Discharge multiplier = 10.4 Discharge volume = 318 x 13.5 = 3,308 cu in. Suction volume = 318 x 10.4 = 4,294 cu in. Calculate bottle dimensions. For elliptical heads, use Equation 14. Bottle diameter db =i 0.86 X v01urnel/~ Volume = suction or discharge volume Suction bottle diameter = 0.86 x 4,2941/3 = 13.98 in. Discharge bottle diameter = 0.86 x 3,30P3 = 12.81 in. Bottle length = Lb = 2 X db Suction bottle length = 2 x 13.98 = 27.96 in. Discharge bottle length = 2 x 12.81 = 245.62 in. Source E, = 0.97 - [(l/l) x (1.617)1'1*8s - 11 X 0.257 - 0.03 Brown, R. N., Compressors-Selection 6 SMng, Houston: = 0.823 Gulf Publishing Company, 1986. 116 Rules of Thumb for Mechanical Engineers 1000 zoo0 3000 roo0 1000 1000 yo00 COMPRESSIBILlTY CHART FOR NATURAL GAS 060 SPECIFIC GRAVITY Y roo0 1000 9000 IO 000 PRESSURE- PSIA 1 , . I a a !. . s. I a s n I I*. . I KILOPASCALS 45,000 50.000 55.000 60.000 65,000 Figure 5. Compressibility chart for natural gas. Reprinted by permission and courtesy of lngersoll Rand. I10 r I40 I so I20 IK) Pumps and Compressors 117 Compression horsepower determination The method outlined below permits determination of 5. approximate horsepower requirements for compression of gas. 1. 2. 3. 4. From Figure 6, determine the atmospheric pressure in psia for the altitude above sea level at which the compressor is to operate. Determine intake pressure (P,) and discharge pressure (Pd) by adding the atmospheric pressure to the corre- sponding gage pressure for the conditions of compres- sion. Determine total compression ratio R = Pd/P,. If ratio R is more than 5 to 1, two or more compressor stages will be required. Allow for a pressure loss of approxi- mately 5 psi between stages. Use the same ratio for the same ratio, can be approximated by finding the nth root of the total ratio, when n = number of stages. The exact ratio can be found by trial and er- ror, accounting for the 5 psi interstage pressure losses. Determine the N value of gas from Figure 7, ratio of specific heat. 6. each stage. The ratio per stage, so that each stage has 7. Figure 8 gives horsepower requirements for compres- sion of one million cu ft per day for the compression ratios and N values commonly encountered in oil pro- ducing operations. If the suction temperature is not 60"F, correct the curve horsepower figure in proportion to absolute temperature. This is done as follows: HP x 460" + Ts = hp (corrected for suction 460" + 60°F temperature) where T, is suction temperature in "E Add together the horsepower loads determined for each stage to secure the total compression horsepower load. For altitudes greater than 1,500 ft above sea level apply a multiplier derived from the following table to determine the nominal sea level horsepower rating of the internal combustion engine driver. PRESSURE (PSI.) Figure 6. Atmospheres at various atmospheric pressures. From Modern Gas Lift Practices and Principles, Merla Tool Corp. 118 Rules of Thumb for Mechanical Engineers Figure 7. Ratio of specific heat (n-value). 70 65 60 55 50 I- I W c-? = 45 II: 4 -1 2 40 35 -I 0 z 30 25 20 15 N: RATIO OF SPECIFIC HEATS CplCv PS: SUCTION PRESSURE IN PS.1.A. PD: DISCHARGE PRESSURE IN RS.1.A. R: COMPRESSION RATIO Pd IPS Figure 8. Brake horsepower required for compressing natural gas. :: 1.10 1.20 1.30 Altitude-Multiplier Altitude-Multiplier 1,500 ft 1.000 4,000 ft 1.12 2,000 ft 1.03 4,500 ft 1.14 2,500 ft 1.05 5,000 ft 1.17 3,500 ft 1.10 6,000 ft 1.22 3,000 ft 1.07 5,500 ft 1.20 8. For a portable unit with a fan cooler and pump driven from the compressor unit, increase the horse- power figure by 7112 % . The resulting figure is sufficiently accurate for all pur- poses. The nearest commercially available size of compres- sor is then selected. The method does not take into consideration the super- compressibility of gas and is applicable for pressures up to 1,000 psi. In the region of high pressures, neglecting the de- viation of behavior of gas from that of the perfect gas may lead to substantial errors in calculating the compression horsepower requirements. The enthalpy-entropy charts may be used conveniently in such cases. The procedures are given in sources 1 and 2. Example. What is the nominal size of a portable com- pressor unit required for compressing 1,600,000 standard cubic ft of gas per 24 hours at a temperature of 85°F from 40 psig pressure to 600 psig pressure? The altitude above sea level is 2,500 ft. The N value of gas is 1.28. The suction temperature of stages, other than the first stage, is 130°F. Pumps and Compressors 119 Solution. 1.05 (129.1 hp + 139.7 hp) = 282 hp Try solution using 3.44 ratio and 2 stages. 1st stage: 53.41 psia x 3.44 = 183.5 psia discharge 2nd stage: 178.5 psia x 3.44 = 614 psia discharge Horsepower from curve, Figure 8 = 77 hp for 3.44 ratio 77 h~ 1,600,000 = 123.1 (for WF suction temp.) 1,ooo,ooo 1st stage: 123.1 hp x 460 + = 129.1 hp 460 + 60” 2nd stage: 123.1 hp x 460 + 130” = 139.7 hp 460 + 60” 1.075 x 282 hp = 303 hp Nearest nominal size compressor is 300 hp. Centrifugal compressors The centrifugal compressors are inherently high volume machines. They have extensive application in gas transmis- sion systems. Their use in producing operations is very lim- ited. Sources 1. E@dw Data Book, Natural Gasoline Supply Men’s Association, 1957. 2. Dr. George Granger Brown: ‘‘A Series of Enthalpy-en- tropy Charts for Natural Gas,” Petrohm Dmemt and Tahmbgy, Petroleum Division AIME, 1945. Generalized compressibility factor The nomogram (Figure 9) is based on a generalized com- pressibility chart.l It is based on data for 26 gases, exclud- ing helium, hydrogen, water, and ammonia. The accuracy is about one percent for gases other than those mentioned. ‘Ib use the nomogram, the values of the reduced temper- ature (TIT,) and reduced pressure (J?/Pc) must be calculated first. where T = temperature in consistent units T, = critical temperature in consistent units P = pressure in consistent units P, = critical pressure in consistent unib Example. P, = 0.078, T, = 0.84, what is the compress- ibility factor, z? Connect P, with T, and read z = 0.948. Source Davis, D. S., P&ohm Refiner, 37, No. 11, (1961). Reference 1. Nelson, L. C., and Obert, E. E, Chem. Engr., 203 (1954). Flgure 9. Generalized compressibility factor. (Reproduced by permission fWro/eurn Ffefiw Vol. 37, No. 11, copyright 1961, Gulf Publishing Co., Houston.) [...]... Efficiency 72.0 68.0 75. 5 72.0 75. 5 75. 5 75. 5 75. 5 78 .5 78 .5 84.0 81 .5 86 .5 84.0 86 .5 84.0 86 .5 86 .5 88 .5 88 .5 88 .5 88 .5 88 .5 90.2 90.2 90.2 90.2 90.2 90.2 90.2 91.7 91.7 91.7 91.7 91.7 91.7 93.0 93.0 84.0 78 .5 84.0 84.0 84.0 84.0 87 .5 86 .5 89 .5 87 .5 90.2 89 .5 91.o 89 .5 91.o 89 .5 91.o 90.2 91.7 91.o 93.0 91.o 93.0 92.4 93.6 91.7 93.6 93.0 93.6 93.0 94 .5 93.6 94.1 93.6 95. 0 94.1 94.1 95. 0 5, 500 6,000 7,000... 97.0 97.3 95. 4 95. 2 95. 5 95. 4 95. 5 95. 4 95. 5 95. 4 95. 6 95. 4 95. 6 95. 5 95. 6 95. 5 95. 6 95. 6 95. 7 95. 6 95. 7 95. 8 89.0 87.0 89.0 88.0 90.0 88.0 89.0 88.0 89.0 88.0 89.0 89.0 89.0 87.0 89.0 88.0 89.0 89.0 89.0 88.0 Table 3 Full Load Efficiencies ~ ~ hP 3,600 rPm 1,200 rPm 600 rpm 300 rPm 5 80.0 82 .5 - 20 86.0 86 .5 - 100 250 - 91.o 91 .5 - 1,000 94.2 5, 000 96.0 - - - 82.7* 91.o 92.0 93.9* 93.7 95. 5* 95. 2 - 93.0... 333P 333G 351 P 428G 357 P A51 G 359 P 359 G 379 P 444G 385P 464G 388P WG 409 P 462G 415P A79G 442 P 442 G 463 P 4 95 G A69 P 50 7 G 465P 465G 496P 5? 4 G 50 6P 602G 496P 496G 52 6P 59 3G 53 4P 617G 53 0P 53 0G 58 8P 613G 56 5P 6S3G ,58 9 P 58 9 G 611 P 648 G l P 66 662 G Spur 1 to1 299 G 3tol 5tol 315P 407 G 319P 434G Helical (1Bdegree) 1 to1 3tol 5tOl 422P 422G 455 P 54 9G 465P 58 1G tain an even number for the total... 3 .5 4.7 5. 1 7.1 7.6 9.7 10 .5 12.7 13.4 18.8 19.7 24.4 25. 0 31.2 29.2 36.2 34.8 48.9 46.0 59 .3 58 .1 71.6 68 .5 92 .5 86.0 112.0 114.0 139.0 142.0 167.0 168.0 217.0 222.0 Efficiency in Percentage at Full Load 4 ,50 0 5, 000 High Efficiency 1 .5 2.0 2.2 2.6 3.0 3.2 3.9 4.8 6.3 7.4 9.4 9.9 12.4 13.9 18.6 19.0 25. 0 24.9 29 .5 29.1 35. 9 34 .5 47.8 46.2 57 .7 58 .0 68.8 69.6 85. 3 86 .5 109.0 1 15. 0 136.0 144.0 164.0 174.0... Rules of Thumb for Mechanical Engineers Very rough efficiencies to use for initial planning below 50 0 horsepower at 3 ,50 0 rpm are Horsepower Efficiency, YO 1-10 10 -50 50 -300 300- 350 350 -50 0 15 20 25 30 40 Some designers limit the speed of the cheaper small steam turbines to 3,600 rpm Sources Figure 1 Typical efficiencies for mechanical drive turbines 1 Evans, E L., Equipment Design Handbookfor Refineries... 0-2 ,50 0 2 ,50 0 -5, 000 5, 000-7 .50 0 7 ,50 0+ Mechanical Losses, L, (%I 3 2 .5 2 1 .5 *There is no way to estimate mechanical losses from gas power requirements This table will however, ensure that mechanical losses are considered and yield useful values for estimating purposes Pumps and Compressors Determine polytropic head, H,: Mechanical losses (L,) L, Hp = Z,RTl(n/n - l)[rp(n-L)'n 1 - 1 = (0.94) (1 ,54 5/ 45. 5) (52 0)(6.88)(3.33)'/".88... turbines steam turbines electric motors centrifugal blowers “Rough” machines include: BHN of Pinion BHN of Gear KaIIFactor Sat 2 25 350 57 5 58 Rc 180 300 57 5 58 Rc 110 35& 450 50 0-800 600 31,00041,000 30,00047,000 45, 000 -55 ,OOO 60,00Ck70,000 The derating factor Cd is used to allow for the manufactured quality, operating conditions, and installation of the gear set Actual gears have tolerance and are not... the precision of the gear tooth form manufactured Select from the columns of Table 5 as follows: v = 262 x d x n (5) Rules of Thumb for Mechanical Engineers 136 Table 5 Dynamic Factor, C, PLV 0-2.000 2,0006,000 5, 000-10,000 Low Quality 1. 35 1 .53 F d-d F Quality Standard Commercial Precision Extra Precision 1.10 1.14 1.20 1. 05 1. 05 1. 05 * > 10.000 1.18 1.26 1.33 1. 25 (7) With the pinion diameter estimated,... (controller) sizes Polyphase Motors NEMA Size 00 0 1 2 3 4 5 6 7 Maximum Horsepower Full Voltage Starting 230 460 -57 5 Volts Volts 1 .5 3 7 .5 15 30 50 100 200 300 2 5 10 25 50 100 NEMA Size 00 0 1 2 3 Maximum Horsepower Full Voltage Starting (Two Pole Contactor) 1 15 230 Volts Volts 1.3 1 2 3 7 .5 1 2 3 7 .5 15 Source 200 400 600 McAllister, E W., Pipe Line Rules of Thumb Handbook, 3rd Ed Houston: Gulf Publishing... 5. 26 x 3 ,50 0 = 4,823 Wmin This is lower than the estimated velocity and would give a C, factor of 1.26 from Table 5 However, this would only reduce the diameter of the pinion by 2%, so there is no need to recalculate Rules of Thumb for Mechanical Engineers 138 Per Equations 8 and 9: F = 1.0 x 5. 26 = 5. 26 in D = 5. 26 x 5. 0 = 26.32 in C= 5. 26 + 26.32 = 15. 79 in 2 Next, the size and number of teeth for . 164.0 174.0 21 4.0 72.0 68.0 75. 5 72.0 75. 5 75. 5 75. 5 75. 5 78 .5 78 .5 84.0 81 .5 86 .5 84.0 86 .5 84.0 86 .5 86 .5 88 .5 88 .5 88 .5 88 .5 88 .5 90.2 90.2 90.2 90.2 90.2 90.2. 96.6 95. 4 89.0 1,200 96.7 95. 2 87.0 3 ,50 0 1,800 96.6 95. 5 89.0 1,200 96.8 95. 4 88.0 4,000 1,800 96.7 95. 5 90.0 1,200 96.8 95. 4 88.0 4 ,50 0 1,800 96.8 95. 5 89.0 1,200 97.0 95. 4 88.0 5, 000. Rules of Thumb for Mechanical Engineers Figure 7. Ratio of specific heat (n-value). 70 65 60 55 50 I- I W c-? = 45 II: 4 -1 2 40 35 -I 0 z 30 25 20 15 N: RATIO