CHAPTER X CAPACITY OF REFRIGERATING MACHINES (Part 3)

piston I travel from Table 13 f = 1.969 cubic feet J Displacement" efficiency of compressor =0.762 Cu. ft. per min. per ton per 24 hours from Table XIV =3.85 - = llltonfl Digitized by V^OOQIC 142 ELEMENTARY MECHANICAL REFRIGERATION TABLE XIII.- ■DISPLACEMENT D IN CUBIC FEET PER FOOT OF PISTON TRAVEL FOR VARIOUS-SIZED CYLINDERS Cubic Fxbt per Foot of Pibton Tbavbl la k "'l| -1^ |i' - OInch KInch HInch ^Inch |g OInch Hlnch HInch Hlnch 1.... 0.00045 0.00071 0.00102 0.00139 1.... 0.00540 0.00852 0.01224 0.01668 2.... 0.00182 0.00230 0.00284 0.00344 2.... 0.02184 0.02766 0.03408 0.04128 3.... 0.00409 0.00480 0.00557 0.00639 3.... 0.04908 0.05760 0.06684 0.07668 4.... 0.00727 0.00821 0.00920 0.01025 4.... 0.08724 0.09852 0.11040 0.12300 6.... 0.01136 0.01253 0.01375 0.01503 5.... 0.13632 0.15036 0.16500 0.18036 6.... 0.01636 0.01775 '0.01920 0.02071 6.... 0.19636 0.21300 0.23040 0.24852 7.... 0.02227 0.02389 0.02557 0.02730 7.... 0.26724 0.28668 0.30684 0.32760 8.... 0.02909 0.03094 0.03284 0.03480 8.... 0.34908 0.37128 0.39408 0.41760 9.... 0.03682 0.03889 0.04102 0.04321 9.... 0.44184 0.46668 0.49224 0.51852 10. . . . 0.04546 0.04775 0.05011 0.05252 10.... 0.54540 0.57300 0.60132 0.53024 11.... 0.05500 0.05752 0.06011 0.06275 11.... 0.66060 0.69024 0.72132 0.75300 12.... 0.06545 0.06821 0.07102 0.07389 12.... 0.78540 0.81850 0.85224 0.88668 13.... 0.07681 0.07980 0.08283 0.08593 13... 0.92172 0.95760 0.99396 1.03116 14.... 0.08908 0.09229 0.09556 0.09888 14.... 1.0689 1.10748 1.14672 1.18556 16.... 0.10226 0.10570 0.10920 0.11275 15... 1,2271 1.26840 1.31040 1.35300 16.... 0.11636 0.12002 0.12374 0.12752 16... 1.3963 1.44024 1.48488 1.53021 17.... 0.13135 0.13525 0.13919 0.14320 17.... 1.5762 1.62300 1.67028 1.71840 18.... 0.14726 0.15138 0.15556 0.15979 18.... 1.7671 1.81650 1.86672 1.91748 19.... 0.16408 0.16843 0.17283 0.17729 19.... 1.9689 2.02116 2.07396 2.12748 20. . . . 0.18181 0.18638 0.19101 0.19570 20.... 2.1817 2.13656 2.29212 2.34840 21.... 0.20044 0.20524 0.21010 0.21501 21.... 2.4053 2.46288 2.62120 2.58012 22.... 0.21998 0.22501 2.23010 0.23524 22.... 2.6397 2.70072 2.76120 2.82280 23.... 0.24044 0.24569 0.25100 0.25637 23.... 2.8852 2.94828 3.01200 3.07644 24.... 0.26180 0.26728 0.27282 0.27842 24.... 3.1416 3.20736 3.27364 3.34104 26.... 0.28407 0.28978 0.29555 0.30137 25.... 3.4088 3.47736 3.54666 3.61644 26.... 0.30725 0.31319 0.31918 0.32523 26.... 3.6870 3.75828 3.83016 3.90276 27.... 0.33134 0.33750 0.34373 0.35000 27.... 3.9760 4.05000 4.12476 4.20000 28.... 0.35634 0.36273 0.36918 0.37568 28.... 4.2760 4.35276 4.43016 4.50816 29.... 0.38225 0.38886 0.39554 0.40227 29.... 4.6870 4.66632 4.74648 4.82524 30. . . . 0.40906 0.41591 0.42281 0.42977 30.... 4.9081 4.99092 5.07372 6.15724 Cooling Effect Produced on Brine A method which avoids opportunity for error in determining the compressor displacement eflBciency, but at the same time intro- duces another diflSculty in the form of Brine-tank insulation losses — ^which fortunately can usually be more or less accurately determined and corrected for — ^is to check the apparent perfor- mance of the compressor by the actual performance of the refrig- erating system as a whole, as determined by direct measurement of the cooling effect produced on brine, where it is regularly em- ployed in the plant, or on brine, water, or some other fluid of known specific heat where a secondary medium has to be introduced for the purpose of test. If, in the latter case, the refrigerating efifect cannot be put to useful work, it may be neutralized by artificial Digitized by V^OOQIC CAPACITY OF REFRIGERATING MACHINES 143 n z o 2 8 o § PQ ^ fa ^B 8 o . S si • -£^5- 91°^ i rH Pag « A^ Q -£S^ § ^ ft I « 5S dad A^fa d«o dd d>o S2: d«o o»o ^8 d«o a>co d-* d-* d'^ A^fa com5 is d-* 5$ Is is A^fa deo dco ■*eo 2S dco So deo o 2g ■*o dco ^o deo Clio ON COCO 1-4 fH desi dei dc4 M dei is <4«eo dci dei 55 dei dw ■*eo dei 2^5 eoN dw dcsi OC9 dc« f-eo dw ow 3<3 coo dd 2S d I ^ n Digitized by V^OOQIC 144 ELEMENTARY MECHANICAL REFRIGERATION heat introduced through the agency of a steam coil or electrical resistance. The amount of cooling that a given quantity of brine will do depends not only upon the number of degrees rise in temperature, but upon the density and kind of brine. The most important element in the selection of the kind of brine to use is the temperature to be produced, which fixes the temperatures at which the brine must be circulated. Saturated salt brine, by which is meant brine so strong that it will dissolve no more salt, freezes at about 5"^ Fahrenheit below zero and would be safe for brine-tank temperatures above zero. The weaker the brine the higher the temperature at which it freezes, the limit being reached when the amount of salt is reduced to nothing, in which case the brine becomes water and freezes at 32° Fahrenheit. Saturated calcium brine freezes at about 55° Fahrenheit below zero and according to its densities is adapted to brine temperatures from 40° below zero up. The specific heat of either salt or calcium brine upon which depend their refrigerating capacities per pound per degree rise in temperature, decreases as the strength increases. The refrigerating capacity of water per pound per degree rise in temperature is one British thermal unit. As salt or calciimi chloride is added to the water this value decreases until its value at saturation (maximmn strength) is only 0.77 B.t.u. In the latter case, about 30 per cent more brine must be circulated, to accomplish a given amount of cooUng for a given rise in brine temperature, than would be necessary were the desired temperatures sufficiently high to allow water to be employed instead of brine as the medium for conveying heat. Approximate Cooling Effect Twenty-five Heat Gallons PER Ton For ordinary accuracy 25 "heat gallons" is considered equiva- lent to a ton of cooling effect, a "heat gallon" being the cooling effect required to reduce the temperature of 1 gallon of calcium chloride brine, of 1.2 specific gravity, through a range of 1° Fahren- heit per minute. The volume of brine circulated expressed in cubic feet per min- ute can be calculated from the dimensions and strokes per minute of the pump, due allowance being made for slippage, and this can Digitized by V^OOQIC CAPACITY OF REFRIGERATING MACHINES 145 be readily converted into weight by multiplying by the weight of brine per cubic foot as given in the accompanying tables. TABLE XV.— PROPERTIES OF CALCIUM CHLORIDE BRINE Salt Required Freeaing Point Amm. Gauge Pressure Lbs. Degrees Salinometer at 60°F. 5«i3 1^. % 1 Lbs. per Gallon Cu. Ft. Dej^ees Degeea yi SH +29 -1.6 43 12 3 1.024 0.980 3 1 7^ --27 -2.8 39 27 6 1.041 0.964 5 IJ^ 8H --25 -3.9 37 36 9 1.058 0.936 7 1/4 11>I --23 -5.0 35>4 40 10 1.076 0.911 9 IM 13 --21 -6.1 34 44 11 1.085 0.896 10 2 15 --18 -7.8 30>4 52 13 1.103 0.884 12 2H 17 -14 -10.0 26 62 15 1.121 0.868 14 19 +4 -15.5 18 80 20 1.159 0.844 18 3 22>4 -1.5 -18.2 12>4 88 22 1.179 0.834 20 3>4 26 -8 -22.2 8 95 24 1.199 0.817 22 4 30 -17 -27.2 4 104 26 1.219 0.799 24 4>4 34 -27 -32.8 1" Vacuum 112 28 1.240 0.778 26 6 37>4 -39 -39.4 8" " 120 34 1.305 32 6>4 41 -54 -47.7 15" " Max. D en., 32 1.283 30 TABLE XVI.— PROPERTIES OF SODIUM CHLORIDE BRINE Salt Required Freezing Point Ajnm. Gauge Pressure Lbs. t III 1 Lbs. per Gallon Lbs. per Cu. Ft. Degrees Degees 0.084 0.63 -f30.5 -0.8 45 4 1 1.007 0.992 1 0.169 1.26 --29.3 -1.6 43.5 8 2 1.015 0.984 2 0.212 1.58 --28.6 -1-5 42.5 10 3 1.019 0.980 2.5 0.256 1.92 --27.8 -2.^3 42 12 3.5 1.023 0.976 3 0.300 2.24 --27.1 -2.7 41.5 14 4 1.026 0.972 3.6 0.344 2.57 --26.6 -3.0 40 16 4.5 1:030 0.968 4 0.433 3.24 --25.2 -3.8 39 20 5.5 1.037 0.960 5 0.523 3.92 --23.9 -4.5 37.6 24 6.5 1.045 0.946 6 0.617 4.63 -22.5 -4.7 35.5 28 7.6 1.053 0.932 7 0.708 5.3 "21. 2 -5.3 34.5 32 8.7 1.061 0.919 8 0.802 6.0 -19.9 -6.7 33 36 9.7 1.068 0.905 9 0.897 6.7 --18. 7 -7.4 31.5 40 10.7 1.076 0.892 10 1.092 8.2 -16.0 -8.9 29.2 48 12.6 1.091 0.874 12 1.389 10.4 H-12.2 -11.0 25.5 60 15.7 1.115 0.855 15 1.928 14.4 -f6.1 -14.7 20.3 80 20.4 1.155 0.829 20 2.376 17.78 +1.2 -16.5 16.5 96 24 1.187 0.795 24 2.488 18.68 +0.5 -17.3 16 100 25 1.196 0.783 25 2.610 19.5 -1.1 -4.7 -18.2 -20.1 14.8 12.5 25.8 1.204 0.771 26 29 Example: — It is found by test that the brine pump of a brine- circulating system discharges 1,000 gallons of brine per minute, the temperature of the warm return brine being 7® Fahrenheit * The specific gravity of a substance is the ratio of the weight of that sub- stance to the weight of the same volume of pure water at its temperature of maximum density at 39 degrees Fahrenheit, at which temperature it weighs 62.425 pounds per cubic foot. The weight per cubic foot of brine given in the table is determined by multiplying 62.425 by the specific gravity as determined by a salinometer or other similar hydrometric instrument. Digitized by V^OOQIC 146 ELEMENTARY MECHANICAL REFRIGERATION higher than the outgoing cold brine. One thousand gallons and 7° rise is equivalent to 7,000 heat gallons, which, divided by 25, the approximate number of heat gallons per ton, gives 280 as the approximate tonnage capacity at which the system is oper- ating. This rule is intended to apply roughly to brines of the higher densities, and, since it does not take into consideration possible variations in the value of the specific heat of the brine, it cannot be expected to apply accurately to brines of all densities. For ex- ample, according to formula [15] the amount of refrigeration pro- duced by the circulation of 200 pounds of water per minute with a rise in temperature of 1° Fahrenheit would be ^ 200X1X1 ^ r= — ;;;3r— = 1 ton. 200 According to the rule, which ignores the specific heat of water, which is unity, the cooling effect would be, since 200 pounds of water is 24 gallons, (Gals, per min.) =—^q oa to (No. of heat gals, per ton) 25 Actual Cooling Effect If we have the specific information that the brine is of a density of 120° salinometer, corresponding to a specific gravity of 1.305, weighing 1.305X62.425 = 81.464 pounds per cubic foot, and that the specific heat of the brine of this density is .767, the cooling effect expressed in tons per 24 hours will be f oimd by the following equation. [15] r= — m which W = Weight of brine circulated per minute. /S = Specific heat of the brine. (<i—fe) = Range in temperature cooled through. 200 = Number of B.t.u. per minute equivalent to a ton of refrigeration per 24 hours. Since there are 7.48 United States gallons in a cubic foot, the weight of the brine per gallon is 1.305X62.425X7.48 = 10.89 pounds, and since 1,000 gallons is circulated per minute the weight (TF) to be substituted in the foregoing expression is 10,890. From Digitized by V^OOQIC CAPACITY OF REFRIGERATING MACHINES 147 the table we find that the specific heat of brine of 1.305 specific gravity is 0.767 and since the range through which the brine is cooled is 7® Fahrenheit, we have 10.890X0.767X7 ^^^„, T<m8 = — = 292.34 tons. 200 For accurate determinations of the cooling effect the density of the brine should be determined by either a saUnometer or some other form of hydrometer that will allow either the percentage of saturation or the specific gravity of the brine to be determined. In taking such hydrometer readings care should be taken to bring the temperature of the brine to that at which the instrument is calibrated. This method is less likely to lead to error than that of applying a correction factor for reducing the readings taken at other temperatures to what they would be if taken at the standard temperature. For very accurate determinations the amount of brine cooled should be determined by weighing and its specific heat determined by some competent expert. Thermometers used in taking the temperatures of the secondary medium before and after cooling, as well as all other apparatus, should be carefully calibrated, both before and after the test. Digitized by V^OOQIC