Document 37GM03GK5eR12xyB957wQRaBx

30 CHAPTER 3 1965 Guide And Data Book Tables 3 and 4 show properties of wati>r for temperatures above 212 F. These tables were abstracted from the steam' tables of Keenan and Keyes.4 DEGREE OF SATURATION AND ITS USE / IN CALCULATIONS At given values of temperature and pressure, the humidity, ratio W of moist air may have any value between aero (dry. air) and W, (moist'air at saturation)! For convenience, a pa- rameter p called degree of saturation is introduced through'the use of Equation 1. . W - pW, (i) To a degree of approximation within the estimated:uncer tainty of data in Table 1, at temperatures below about 150 F,: the volume t> of moist air per pound of dry air may be com puted by Equation 2. i.**+/. (2)' To 'obtain comparable accuracy, at temperatures above about 150 F, it is necessary to.add a correction term e as. follows: . .t ~ --m)A ' . A*.* 1.6078 pW,' (3)- At temperatures bdow1150 F, the enthalpy A of moist air per pound of dry air may be computed by Equation 4. A " hm -f;./AM . (4) To obtain comparable accuracy at temperatures-above' about 150 F, it is necessary to add a correction term A as follows: .. n(l -- p)B . 1 + 1.6078 pW, (5). ' Unfortunately, values of entropy s oi moist air per pound: of.dry air computed by.the relation , " + ' * 4 (6) dp not approximate the. true values as closely as might be desired-except at temperatures considerably telow 150 F. Only a small portion of the error is compensated for by the' correction term. ' ' . ud.-pyc. 1 + 1.6078 pW, (h- The larger portion of tiie deviation arises from the mixing- entropy. It can be expressed as an additional correction'1term as follows: - f - 0.1679 [(1 + 1.6078 pW.) logs, (1 + 1.6078 pW, - 1/6078 pW. logi, ,,) . - >(1 + 1;6078 W.) log,, (1 + 1.6078 W.)} (8) Table S.showB values of the coefficients A, B, and .C- in/ Equations 3, 5, and 7 respectively and marimum values of tiie correction terms *, A, j, and i. - THERMODYNAMIC WET-BULB TEMPERATURE / For any state of moist air, there exists a temperature.f* at which liquid (or solid) water may be evaporatedinto tiie air to bring it to saturation>at exactly this same temperature, fig. 8 may be used as a schematic representation of the adiabatic saturation -process where the leaving air is satu rated and is at a'temperature equal to that of the injected water. In`the process, 'the humidity ratio is increased from a' given initial value IFtothe value Wt* corresponding to satii- ration at the temperature t*; the entiiaipy is increased from a given initial value A to the value A,* corresponding to satura tion at the temperature <*; the weight of water added per v pound of dry air is (TP,* -- W) which adds energy to the moist air of amount:(TP,* - W)hJ, where A* denotes the specific enthalpy of the water added at the temperature f*. Therefore, if the process is strictly adiabatic, conservation of energy requires that: > _ ... * + (IF,* - W)K* - A,*(9) The properties TP,*, hj*, and A,* are functions only of the temperature t* for a fixed value of pressure. The value of t* which satisfies Equation 9 for given values of A and TP is called thermodynamic wet-bulb temperature. The psychrometer is a device consisting'of two thermome-' tera, one of which has its'bulb covered with'a suitable Wick that has been thoroughly wetted with water'/ When the weti1 bulb is placed in an air stream; water may evaporate from the' wick. The equilibrium temperature eventually reached by the water is called the wet-bulb temperature.' This process is hot the same as one of adiabatic saturation which /defines' the thermodynamic wet-bulb temperature; but rather is; one of simultaneous heat and mass transfer from the we+bulb/The' fundamental mechanism of this'process ^`described in'Ghap? ter 5, Mass Transfer. Fortunately, and indeed fortuitously, the corrections to be applied to readings of a WetJwilb ther mometer to obtain the thermodynamic wet-bulb,temperature' are usually quite small.- Arnold* has presented a . procedure which allows calculation of these corrections.'- y Example I: Find the degree of saturation, humidity ratio * eothalpy; and volume of moist air at 90 F dry-bulb temperature, 63 F thermodynamic wet-bulb temperature, and 29.921 in/'Hr pressure. * Solution: From/Equations 1; 4, and,9. \ :-j - :T (A. + Phj +!(F,*.- pW.)hS - *,* Inserting numerical data from Table 1 gives: ......... -. (21.625 + 34.31,.) '+ (0.01235 - 0.03118,0(31.12) - 28.57 and . ': ' From Equation 1 p - 0.1967 .......>h:i * TP - (0.1967)(0.03118) -0.006133 Ib.water/lb dry-airi From Equation4 '' -2 A " 21.625 + (0.1967) (34.31) - 28.37 Btu/lb dry air'-. From Equation 2 f - 13.853 + (0.1967)(0.692) '-- 13/989 cu ft/lb'diy air, " PERFECT GAS RELATIONS * Tables 1 and 5,.with Equations 1 to 9, allow accurate cal-; culations of moist air properties where sea-level pressure may be assumed.; The equations of Goff and Gratch may be used to. calculate tables similar to Table l.for any .pressure, but; as yet such tables are not available.- Fortunately, only slight' errors occur when Dalton's Rule and perfect-gas-,relations are applied where normal barometric pressures ;i. According to Dalton's Rule, if.dry air and-.water vapor are. mixed, each occupies the whole volume of tiie nrnt*jnr>r at the1 temperature.of the mixture, and-the pressure of the:mixture is the sum of the individual pressures. Assuming;that both dry air and water vapor behave like perfect gases, the volume sr occupied by rw mols of dry air at temperature:T.ftnd pres sure p, is: .............. .. . . nRT or P. (10) Psychrometrics^ 31 "--u Table ! .. Thermodynamic Properties of MOiST A/k* (Standard Atmospheric Pressure, 29.921 in. Hg) Fdtt. Temp. Humidify Ratio w.xto*, Volume 9 ft/tb dry ab afMpy Btu/lb dry air h. ; h, Bfv peri*F) (/b dry air) Condensed Water ,4- fahr. . . Enthalpy Btw/lb he Entropy . ''op press CflOM In. Hg * p. X 10* temp. HFl 7.630 7.647 7.775 8X29 8.156 8.2S3 8.411 0.01606. 0.02571 0.04063 0.06340. 8.537 8.664 8.792 8.919 0.09773 . 9-046 0.1489 . 9.173 0-3343 - 9.300 0.3343 . 9.436 0.4930 - 9.553 0.7196 - 9.680 '1.040 9.806 .1.49! 9-933 10.059 10.186 10.313 5.406 6.149 6.985 7.935 8.980 10.16 11.49' 13.93 10.414 10.465 10.510 10.506 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000' 0.000 0.001 0.00! 0.001 0.001 0.001 0.001 -7.520 . 7.647 7.775 7.902 8.029 8.156 8.383 -8.411 10.166 10.314 : 10.385 10.415 10.466 10.517 10.567 10.619 .10.670 10.730 10.771 -38.504 -37.296 --36-089 -34.881\ 0.000 ,0X00 0.000 0.000 -38.604 -37.296 -36.088 -34.831 -0.10300 --0.09901 -0.09503 -0.09121 -33.674 -32.466 -21.263 -30.0J7 <0.000 0.000 0.000 0.000 -33.674 -32.468 -31.263 -30.057 -0.087(0 -0.08365 -0.07997 -0.07634 -28.652 -27.6(8 -26.4(4 -25.240- `0.000- <0.000 . 0.0000.001 --2S.8S3 -27.648 -26.444 -25.239 -0.07277 -0.00924 -0.06577 -0.06234 -24X37 --22.835 -21.631 -20.498 0.001 0.00.0-002 0.003 . -24.036 -22.833 -31.629 -20.425 -0.05897 --O.OSS65 -0.05237 -0.04913 -19.226 -18.023 -16.820 --15.617 0X0S 0-007 0X11. 0.016 -19.220 -18X15 -16.809 -15.602 -0.04595 -0.04280 -0.03969 -0.03063 -14.416 -- 13.214 -12.012 -11.632 0.022 0.031 0.043 . 0.049 -14.294 -13.183 --11.909 -11.483 -0.03300 -0.03001 -0.02766 -0.02649 -11.051 -10.571 -10.090 --9.609 0.056. 0.064 0.073< 0.083 -10.995 -10.507 -10.017 -9.528 -0.02533 -0.02416 .-0.02301 -0-02186 -9.129 -8.648 -6.168 -7.687 0.094 0.106 0.121. 0.t36 . -9.035 `-8.542 -8.0(7 -7.551 --0.02072 -0X1958 -0X1845 -0.01733 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00001 0.00001 0.00001 0.00003 0.00003 0.00005 0.00000 0.00009 0-00012 0.00013 0.00014 0.00016 0.00019 0.00031 0.00024 0.00028 0.00030 0.00034 -0.10300 -0.09901 -0.09508 -0.09121 -29.00 220.40 -218.77 -217.13 --0.4907 -0.4853 -0.4800 -0.4747 0:0001009 0.0001843 0.0003301 0.0005807 -0.08740 -0.08365 -0.07997 -0X7634 -216.44 -313.76 -212.03 -310.28 --0.4695 -0-4642 -0.4590 -0.4538 0.001004 0:001707 0.002853 0.004710 -0.07277 -0.06934 -0.06577 -0.06234 -208.59 -206.73 -304.92 -203.09 -0.4485 -0.4433 -0.4381 -0.4329 0.007653 0.01226 0.01939 0.03026 -0.05897 -0.0S56S -0.05236 -0.04912 -201.23 -199.35 -197.44 -195.51 -0.4277 -0.4225 -0.4173 --0.4121 0.04666 0.07111 0.1071 0.1597 -0.0(694 -0.04278 -0.03966 -0.03658 -193.55 -191.57 -189.56 .-187.53 -0.4069 -0.4017 -0 3965 -0.3913 0.2356 0J((1 6.(976 0.7130 -0.03354 --0.03052 -0.02754 -0.02836 --185.47 -0.3881 1.0127 .-183.39 -0.3810 1.4258 -181.29 ^0.3758 1.9910 v. -180.44' ;H>.37$8 2.2702 ; -0.02518 -179159 --0.02(00 -178.73 -0.02383 --177.87 -0.02165 -177X1 -O.J7I7 -0.3696 -0.3876 -0.3655 2.5854 3.9409 3.3408 3.7906 -0.020(8 -9.01933 -r0.01815 -0.01699 -176.14 -175.27 -174.40 -173.52 -0-3634 4.2958 -0.3614 4.8626 -0.3593 6:4960 -0.3572 6.2093 Hvmidrty Ratio W. X to4 Volume b ft/tb dry air Btii/tb dry air 6fu par (*F) (lb dry air) Condensed Water Enthalpy Bhi/Lb hm Entropy Bfu per maw Vap. Preu In. Hg P. X 10* fahr. Tt?r . 1.649 ` 1.656 1.087 3.344 . 3.630 3.7851.948 3.130 3.301 3.491 ..3.693 3.903 4.135. 4.369 4.606 4.865 5.137 6.433 6.734 - 6.040 6.371 6.730 7.085 .7.469 . 7.873 8.195' 8.739 10.820 10.870 10.921 10.971 11.149 11.174 -11.200 .11.325 11.350 11.375 11.301 11.326 11.351 11.376 11.401 : 11.437 11.654 11.679 .11.70$ 11.730 0.003 0.003 0.003 0.004 0.004 0.005 0.005 .0X08 . 0.006 0.006 0.007 0.009 : 0.010 j 0X10 0.011' . 0.013 0.013 0X13. 0.014 0.015 ' 0X15 0.016 0.017 ; 0.018 ' 0X19 10.873 10.924 10.976 11.078 11.103 11.129 11.155 11.180 11.306 11.232 11.359 11.385 11.411 11.437 tl.463 11.489 11.515 11.541 11.671 11.697 11.734 11.750 -7.207 .-6.726 -6.246 .-6.75$ -5.285 -.4.804 --4.564 -4.334 -3.123 -3.882 -2.643 -0.240 0.000 0.240 0.480 . 0.721 0.961 1.201 1-441 Compiled by John A. Goff end S. Qretch- 0.154 0.173 0,198.. 0.219 0.3381 0.348 0.368 0.413 0.436 0.461 0.487 0.614 . 0.543 0.574 0.606 -7.053 -6.553 -6.060 -5.646 -5.039 -4.627 -4.371 -4X14 '-3.755 -3.495 -3.235 -3.974 -3.711 -3.446 -3.181 -1.916 -1.379 -1.107 -0.835 0.675 . 0.713.; 0.751 - -0.01621 -0X1509 -0.01398 -0.01387 -0.01177 -0.01067 -0.01012 -0.00958 -0.00263 -0.00210 -0.00157 -0.00105 0.00099 0.00104 0.00109 0.00116 o.oom 0.00128 0.00135 0.00142 0.00149 0.00157 0.00165 0.00174 0.00183 0.00192 0.00202 0.00212 1.991 3.238 3.583 0.00234 0.00246 0.0B2S8 --0.01583 -0.01466 -0X1350 -0X1233 -0.01116 -0-00999 --0.00940 -0.00883 -0.00766 -0.00707 -0.00649 -0.00590 -0.00532 -0.00473 --0.00(14 -0.00354 -0.00294 -0.00234 -0.00174 0.00131 0.00192 0.00254 0.00316 -171.75 -170.88 -169.97 0.3553 -0.3531 -0.3511 -168.17 -187.72 -157.28 -0.3469 -0.3449 -0.3439 -0.3428 -166.81 -166.35 -165.90 -165.44 -0.3418 -0.3408 -0.3398 -0.3387 -164.98 -164.52 -164.06 -163.60 -0.3377 -0.3337 -0.3357 -0.3349 -163.14 -162.67 -163.31 -161.74 -0.3338 -0.3328 -0.3315 --0.330S -161.28 -160-81 -160.84 -169.87 -0.2295 --0.3285 -0.3275 -0.3264 -159.40 -0.3254 -15B.93 -0.3244 -158.46 -0.3234 -157.63 -157.04 -156-57 -1S6.09 -0.3213 -0.3203 -0.3193 -0-3182 1.4929 1.6795 1.6706 1.7566 1.8677 1.9740 2.0859 3.2035 2.3272 2.4573 3.6940 3.7377 3.0479 3.9137 3.3SS5 3.6790 3.7645 3.9666 4.1785 4.4007 4.6337 4.8779