# Rational Psychrometric Formulae/Appendix No. 2

APPENDIX No. 2
EXPERIMENTAL DEMONSTRATION OF THE FOUR PSYCHROMETRIC PRINCIPLES GIVEN IN PARS. 30 AND 31
72While the four psychrometric principles might be all logically surmised, experimental demonstration is desirable. A calorimetric method was devised
Fig. 11 General View of Apparatus.
by the author for this purpose and also to determine the probable error of the indications of the wet bulb in the sling psychromcter due to radiation.
73The apparatus used is shown in Figs. 11, 12 and 13. Air was supplied by fan A at slight pressure to the wooden air duct B, from which it escaped through the oriﬁce C, and through the tube D, in which the wet-bulb ​calorimeter, Figs. 11 and 12, was used in different experiments. A differential draft gage and pitot tube indicated the velocity of the air through the oriﬁce and over the wet-bulb thermometer No. 4.
74This velocity could be varied any desired amount between 1000 and 4000 ft. per min. by adjustment of the motor rheostat. It was found that the static pressure in the box agreed substantially with the velocity head at the thermometer bulb so that no further measurements of the former were recorded. Thermometer No. 1 indicated the dry-bulb temperature of the air in the box, thermometer No. 2, the dry-bulb temperature of the air outside, and thermometer No.3, the calorimeter temperature. Thermometers Nos. 3 and 4 were calorimeter thermometers especially constructed for this test by the Taylor
Fig. 12 Plan and Elevation of Apparatus.
Fig. 13 Detail of Calorimeter.
Instrument Company. They were in the fahrenheit scale, graduated to tenths of a degree, and calibrated to 1/40 deg. They were also carefully compared.
75Experiment No. 1. This test was made in order to determine the effect of an air blast of known intensity upon the readings of thermometers No. 3 and No. 4. The need of the determination was evident as the velocities were not necessarily the same upon the two bulbs nor in the same relative direction. Moreover, it was evident that a portion of the heat of the air was converted into mechanical energy of the air current; also that a portion of this, at least, was re-converted into heat by impact on the bulb. This temperature error, if any, would be proportional to the velocity head; therefore a maximum condition of 1-in. velocity head and static pressure were taken. Both thermometers and the calorimeter were perfectly dry. The apparatus was run under constant ​conditions for 1 hour previous to the test. Consecutive readings were taken of marked uniformity, and the average results are given in Table 3.
76The actual calculated drop in temperature due to 1-in. air blast under the above conditions is
$D=(82.7+459.6)\left[1-\left({\frac {397}{398}}\right)^{0.29}\right]=0.38{\text{deg.}}+$
77It will be noted that thermometer No.3 read 0.047 lower than No. 4 at 1 in pressure. However, at a wet-bulb temperature of 70 deg., 1 deg. in the temperature of the dry-bulb produces only 0.3 deg. increase in wet-bulb temperature; i.e., ${\frac {dt'}{dt}}=0.30$. Therefore at 1 in. pressure the error would be 0.014 and at ¼ in. pressure 0.0035. Hence, in any case, the correction would be negligible.
TABLE 3 EFFECT OF AIR. BLAST OF KNOWN INTENSITY ON READINGS OF THERMOMETERS NO. 3 AND NO. 4
| Thermometers | Thermometers | Thermometers | Thermometers | Temperature Differences | Temperature Differences | Temperature Differences |
| No. 2 | No. 1 | No. 4 | No. 3 | 1 and 3 | 1 and 4 | 3 and 4 |
| . . . . . . | 82.797 | . . . . . . | 82.653 | 0.084 | . . . . . . | . . . . . . |
| . . . . . . | . . . . . . | 82.566 | 82.613 | . . . . . . | . . . . . . | 0.047 |
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . | 0.031 | . . . . . . |
| Barometer pressure = 29.3 in. mercury = 397 in. water. |||||||
The temperature increase $E$ produced by an air blast equivelent to $p$ in. of water may be expressed by the equation
$E=\left({\frac {0.38-0.13}{1}}\right)p=0.25p$
or 0.25/0.38 = 66 per cent of the theoretical temperature.
78Experiment No. 2. This was for the purpose of determining approximately the per cent of error due to radiation and stem correction in the depression of the wet bulb of the sling psychrometer, and was accomplished by comparing wet-bulb thermometer No. 4, with wet-bulb thermometer No. 3, which was protected from practically all radiation by surrounding it with insulated wet surfaces at precisely the same temperature, and by protecting the stem with a wet cloth. This arrangement is shown in Fig. 11, and may be termed a wet-bulb or evaporation calorimeter. The protection for the wet bulb consisted in an annular vacuum tube, having the exterior surface covered with a wet cloth, and the interior with a tube of wet blotting paper. This was placed in an open tube leading from the air duct so that there is the same circulation of air over the wet surfaces as over the wet-bulb thermometer placed within. Thermometer No. 4 was rotated while being subjected to the blast, so that the condition in the sling psychrometer would be exactly reproduced.
​79The log of these tests shows that the error in the depression of the wet blub in the sling psychrometer for various velocities is as shown in Table 4 and Fig. 10. This error has been taken as directly proportional to the depression. More accurately it is proportional to the difference of the fourth powers of the respective absolute temperatures, except for the stem correction. However, where the depression is the usual small percentage of the absolute temperature, the error in assuming direct proportionality is insigniﬁcant.
80The sling psychrometer, however, is subject to another error, heretofore seemingly overlooked. As shown in experiment No. 1, there is a rise in temperature due to the impact of the air upon the bulb, which, in the case of the dry bulb is 66 per cent of the theoretical, or $0.25p$, and in the case of the wet
TABLE 4 AVERAGE RESULTS OF TEST FOR RADIATION ERROR IN WET BULB OF SLING PSYCHROMETER :
| 1 | Velocity pressure, in. water | 0 | .08 | 0 | .16 | 0 | .25 | 0 | .55 | 0 | .75 | 1 | .00 |
| 2 | Velocity, ft. per min | 1160 | 1160 | 1640 | 1640 | 2050 | 2050 | 3040 | 3040 | 3550 | 3550 | 4100 | 4100 |
| 3 | Room temperature No. 2 | 85 | .0 | 82 | .0 | 85 | .1 | 85 | .2 | 87 | .2 | 87 | .25 |
| 4 | Dry-bulb temperature No. 1 | 87 | .125 | 83 | .93 | 83 | .88 | 83 | .975 | 88 | .125 | 88 | .59 |
| 5 | Calorimeter temperature No. 3 | 68 | .935 | 69 | .725 | 71 | .158 | 71 | .740 | 68 | .494 | 68 | .830 |
| 6 | Wet-bulb temperature No. 4 | 59 | .21 | 70 | .01 | 71 | .353 | 71 | .892 | 68 | .654 | 68 | .965 |
| 7 | Calorimeter depression (difference between items 4 and 5) | 18 | .19 | 14 | .205 | 12 | .722 | 12 | .285 | 19 | .681 | 19 | .760 |
| 8 | Difference between wet-bulb and calorimeter temperature | 0 | .295 | 0 | .285 | 0 | .195 | 0 | .152 | 0 | .160 | 0 | .136 |
| 9 | Ratio of wet bulb minus calorimeter temperature to calorimeter depression (item 8 ÷ 7) | 0 | .016 | 0 | .020 | 0 | .015 | 0 | .012 | 0 | .008 | 0 | .007 |
| 10 | Item 9 corrected for difference in impact | 0 | .01606 | 0 | .02018 | 0 | .01527 | 0 | .01239 | 0 | .00853 | 0 | .00771 |
| | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ | ${\text{Temperature difference due to impact}}=0.3\times 0.047\times {\text{velocity pressure}}$ |
| | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ | ${\frac {dt'}{dt}}=0.3{\text{at}}t'=69{\text{to}}70{\text{deg. fahr.}}$ |
| | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ | $0.047={\text{temperature difference (thermometer No. 3 - thermometer No. 4)with dry-bulb }}$${\text{thermometers due to difference in impact at 1 in. velocity pressure.}}$ |
bulb, $0.25p{\frac {dt'}{dt}}$. This, however, would have no effect upon the calculated absolute humidity, but only on the temperature and consequent relative humidity.
81The type of psychrometer which lends itself to the most accurate determinations is the Aszmann aspiration psychrometer shown in Fig. 14. Here the air is aspirated through two tubes containing the wet and dry-bulb thermometers. The wet-bulb temperature is brought to a minimum by the use of an atomizer. This serves also to moisten the inner surface of the enveloping tube, thus cooling it and preventing radiation. In this type of psychrometer it should be noted that the impact of the air upon the thermometer bulbs largely neutralizes the reduction in pressure, producing the velocity as demonstrated in experiment No. 1.
​82Experiment No. 3. The purpose of this experiment was to demonstrate principles C and D in Pars. 30 and 31. A modiﬁed form of the evaporation calorimeter as shown in Figs. 5 and 6 was used.“ The air was ﬁrst passed through two layers of moistened sponge, bringing it very close to true
Fig. 14 Aspiration Psychrometer.
adiabatic saturation. Its temperature was then taken alternately with a wet-bulb and a dry-bulb thermometer, and simultaneous readings were taken with thermometer No. 4, the error of which had been established. It was found very difficult to obtain consistent readings to the degree of accuracy desired, on account of the extreme lag of temperature in the calorimeter thus constructed. On this account it was found necessary to maintain the ​temperature constant at No. 4 by continuous hand regulation at the fan inlet and continuous observations of thermometer No. 4. It was found possible in this way to prevent a variation of more than 0.05 deg. Results showed the temperature in the calorimeter with a wet bulb to be a little lower than a No. 3 when a dry bulb was used, owing to slightly imperfect saturation. This test, therefore, did not agree exactly with the results of experiment No. 2. It appeared to be possible, however, for the water on the wet bulb in experiment No.2 to be cooled to a lower temperature than that of adiabatic saturation, and it is necessary, therefore, to attribute this slight discrepancy to some source of error in the temperature of the air in experiment No. 3. Three explanations
TABLE 5 COMPARISON OF WET-BULB TEMPERATURE WITH SATURATION TEMPERATURE WHEN PASSING AIR THROUGH WET SPONGE IN CALORIMETER, PRESSURE 0.25 IN. :
| No. 1 Dry-Bulb Temperature | No. 2 Wet-Bulb Temperature | No. 3 Calorimeter Temperature | Difference |
| 81.75 | 61.90 | 61.80 | 0.10 |
| 81.75 | 61.95 | 61.85 | 0.10 |
| 81.75 | 62.00 | 61.85 | 0.15 |
| 81.75 | 62.05 | 61.90 | 0.15 |
| 81.75 | 62.00 | 61.90 | 0.10 |
| 81.75 | 62.00 | 61.90 | 0.10 |
| 81.75 | 62.65 | 62.65 | 0.00 |
| 81.75 | 62.60 | 62.65 | 0.05 |
| 81.75 | 62.65 | 62.65 | 0.00 |
| 81.75 | 62.65 | 62.625 | 0.025 |
| 81.75 | 62.65 | 62.65 | 0.00 |
| 81.75 | 62.60 | 62.625 | 0.025 |
| 81.75 | 62.65 | 62.65 | 0.00 |
| 81.75 | 62.60 | 62.625 | 0.025 |
| 81.75 | 62.65 | 62.65 | 0.00 |
| 81.75 | 62.60 | 62.65 | 0.05 |
| 81.75 | 62.65 | 62.625 | 0.025 |
| 81.75 | 62.70 | 62.65 | 0.05 |
are possible: (a) the air being thoroughly saturated before entering the tube of the calorimeter, its temperature would easily be increased with any slight adiati on due to imperfect insulation, especially since air delivery was greatly educe d by the resistance of the sponge; (b) at the time the readings were taken the outside was always beginning to get dry, due to the very long time required to bring the temperature of the calorimeter to a minimum, during which the cloth on the calorimeter would begin to dry and require moistening, resulting in a momentarily increase of temperature; (c) the possibility of some parts of the sponge becoming dry and conducting a slight amount of heat to the wet portions.
83The agreement of these tests, however, is quite sufficient to warrant fully the acceptance of the fundamental principles previously stated. It is also made evident that the reading of the wet-bulb thermometer properly protected from radiation as in experiment No. 2 is a most practicable and accurate method of determining the temperature of adiabatic saturation.