HUMIDITY MEASUREMENTS
THEORETICAL CONSIDER 4TIONS
The authors present an approximate correction to the original equation with the understanding that succeeding refinements are not invalidated but must also be appended. On the assumptions of adiabatic Conditions existing on the wet bulb, heat balances may be set up. On one side heat is removed from the wet bulb by vaporization of th water; on the other hand, heat is gained by convection anc. radiation from the surrounding air and walls, It has been postulated that, with a sufficiently high air velocity, the radiation effect on an unenclosed bulb is negligible (2, 6) and ill be neglected in this derivation. The heat transferred by vaporization of the water, p = r W , and under equilibrium conditions must equal the sensible heat transferred to the bulb from the air:
in Presence of
Water-Soluble Salts
where p
= heat transferred per unit of time r = latent heat of vaporization of water W = quantit'y of water vaporized per unit of time
h = air-film heat transfer coefficient A = superficial area over v-hich heat transfer takes place T = temperature of air T , = wet-bulb temperature
G. C. WILLIAMS AND R. J. W-ILLIARIS'
Therefore ( I , 6 ) ,
University of Louisville, Louisville, Icy.
rW
h B ( T - T,)
(2)
The presence of soluble salts in the water of the wet bulb will introduce other factors, which will be taken up separately. The first effects to be considered are the heat of solution and the heat of crystallization of the salt. Equation 2 then becomes:
ET- and dry-bulb psychrometry is one of the most important methods for the determination of humidity. It is commonly used in domestic apparatus as well as in industrial applications, and is the basic mechanism for many air-drying-operation controllers. In the latter case the measured air may be contaminated by particles of water-soluble salts which are carried by the moving gas stream and are almost impossible to remove before the humidity determining device is reached. The need for some method of taking measurements of this type became apparent when a n attempt was made to obtain a heat and weight balance on a rotary dryer handling crystalline trisodium phosphate dodecahydrate in commercial production. It has subsequently been of use in the same capacity when studying the necessary design for a rotary dryer for crystalline copper sulfate. These applications suggested that, since many crystalline water-soluble salts are handled in rotary dryers or kilns, a method of controlling or measuring atmospheric conditions could be very useful. When puch a condition exists, the salts dissolve in the water which surrounds the wet bulb, cause a saturated solution to form, and change the measured wet-bulb temperature. The direction of change is normally to a higher temperature and the reading would indicate an erroneously high humidity in the air stream. Prior to 1911 no accurate method of determining absolute humidity b y means of wet- and dry-bulb thermometry had been developed, nor had any relation, other than empirical, been established between humidity and met- and dry-bulb temperatures. I n 1911 Carrier (2) set forth the basic psychrometric principles of the present-day practice for humidity determinations. The original Carrier equation has been somewhat modified. Errors in the assumption of adiabatic conditions existing on the wet bulb have been proved, corrections have been added, and the equation has been modified to fit the cases of other liquid media in place of water, etc. However, the condition of wet-bulb errors caused b y dissolved salts has apparently been overlooked. 1
=
?"w= h A ( T - T 3 + pa + pc
(3)
where pa = heat evolved by solution per unit of time pc = heat evolved by crystallization per unit of time
As TV is the rate of vaporization, the following relation may be set up according to Fourier's law (4):
w = kg-4(pw - p ) where li,
(4)
= diffusion film coefficient p , = partial pressure of water at wet-bulb temperature p = partial pressure of water vapor in bulk of air
A theory is presented for the observed rise in wetbulb temperatures when measured in atmospheres containing water-soluble salts, and a procedure is advanced for a quick and easy approximation of the true wet-bulb temperature from the observed value. This method reverts to the standard psychrometric charts for the final humidity calculations. Experimental data are presented on four watersoluble salts over a dry-bulb range of 60" C. and a corresponding w-et-bulb range of 40' C. The true wet-bulb depressions varied from 4 ' to 45" C., and the temperature rise of the salt solution effect varied from 0.5" to 8.4"C. The experimental values of salt solution wet-bulb temperatures were converted to water wet-bulb temperatures and show substantial agreement with the experimentally determined water w-et-bulb values.
S o u in t h e United S t a t e s Nary.
730
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
lune, 1943
The heat relation mav then be set -qs
+ ~ ( p w- p ) k J
UD
as
hA(T - Tw)
T A B L E I . DATAAND RESULTS
+ qe
(5)
The heat of solution, q., affects the heat balance only as long as the concentration of salt in the wet-bulb film is below the concentration of the salt in a saturated solution. Under less-than-saturated conditions p , and T, will not be constant but will vary instantaneously as the concentration is increased by evaporation of the water. I n order to set up a valid relation in which T, may be measured aocurately, the wet film must first be saturated. The relation will then become: r ( p w - p)k,A = hA(T
-T3
+ q0
(6)
The quantity of pc is dependent upon the rate of evaporation of the water and is related to the rate of vaporization as follows: q c = CkgA(pw - P) (7 ) where C = heat evolved by crystallization per unit of water evaporated
The relation now is:
The next factor to be considered is the effect of vapor pressure lowering caused by addition of the salt to the water. The effect of the vapor pressure lowering is an increase in the wet-bulb temperature. If the change in vapor pressure from that of pure mater is represented by Ap,, the vapor pressure of the salt solution is: Pa
A-PURE 8-SALT
2
Pw
WATER
SOLUTION
a 0
(1.
> TEMPERATURE
Figure
1.
Evaluation of
- APw But the vapor pressure lowering will result in an increase in t h e w e t - b u l b temperature by a n amount AT, in order that equilibrium be m a i n t a i n e d in the heat transfer to and from the wet bulb. The wet-bulb temperature with a salt solution as the wetting medium is, then,
(TaA--Tw)
T. = T ,
+ ATu
If a series of salts are considered in the order of decreasing solubility, it is evident that the vapor pressure lowering ( A p J for the saturated solutions of these salts will also decrease in the same order. Thus the limit is reached a t zero salt solubility, p = 0, p. = p,; and T, will be the temperature a t which the salt solution will have the same vapor pressure as pure water a t temperature T,. The final form of the equation then becomes - C)(p,
where rs
=
- p)
=
2' - (2'.
731
-
AT,)]
(9)
heat of vaporization corresponding t o T . and approximately equal t o r
The value of (T, - ATw) may thus be obtained from isobaric readings on vapor pressure curves and may be substituted for T, in the basic psychrometric formula (8, 4) t o obtain H (Equation 10).
Soln. Bulb DryTemp.
T,
C. --Sodium 51 56 57 59.3 67 77.3 79 79.2 76.5 75.2 73.2 69.0 31 31.5 31.3 31.5 32.0 32.4 38.2 39.5 41.7 41.5 43 44 45 44 44 49 54 55 55 60.5 62 64 66 22.5
WetBulb Temp. TJ, C. 40 41.5 41.2 41.2 44.5 48.4 50 42 41.7 41 46 45.5 18.7 21.8 21.7 23.7 27.0 31.0 31.1 33.0 36.0 23.8 24.0 28.6 30.0 37.5 32.8 33.6 38.0 42.0 43.0 41.2 41.5 42.9 30.0 16.2
--Ammonium 25 21.3 25 20.9 25 21.1 70 35.5
Ts
-
AT,
Nitrate33.6 35.0 34.8 34.8 37.8 41.2 42.5 35.5 35.5 34.6 39.2 38.7 14.4 17.2 17.1 18.9 22.0 25.5 25.6 27.2 30.3 19.1 19.2 23.4 24.6 31.4 27.0 27.6 31.8 35.5 36.4 34.8 35.0 36.4 24.6 12 Nitrate14.0 13.7 13.8 25.4
Exptl. WetBulb Temp. Twl O
C.
33.0 34.2 33.8 34.2 37.0 40.3 42.5 34.2 33.8 33.2 39.0 38.5 14.3 17.7 17.7 19.7 23.0 27.0 27.0 28.5 31.0 18.3 18.5 24.1 24.7 32.0 27.5 28.0 32.0 36.0 37.0 34.8 35.0 37.1 25.0 12.4
12.9 12.5 12.7 27.8
Soln.
!?I%{g~$ Temp. Temp.
Exptl. WetBulb Temp.
--Potassium 36 19.0 36.2 18.9 38 19.3 39 22.5 39 23.7 39.7 24.6 40.5 27.4 40.5 32.7 40.0 32.6 40.5 20.6 40.5 20.1 41.0 23.7 41.5 25.0 41.9 27.0 40.5 35.0 45.0 34.5 46.2 35.0 47.0 35.5 22.8 13.2
Ta Tu, ATw C. Chlorate-18.5 17.9 18.3 17.9 18.7 18.3 22.0 21.8 23.1 22.9 24.0 24.0 26.9 26.8 32.2 32.1 32.0 32.0 20.0 19.7 19.6 19.4 23.1 23.0 24.4 24.4 26.4 26.5 24.5 34.3 34.0 34.0 34.5 34.5 35.0 35.0 13.1 12.4
-Potassium 28.2 15.9 29.0 21.0 35.0 21.5 40 25.8 42 28.4 44 30.0 44.1 35.0 43.3 39.8 42 39.0 41.4 38.7 42 32.8 44 29.1 45 27.1 45 28.0 29.0 50 53 33.3 56.5 35.0 25.6 15.3
Chloride13.2 18.8 19.3 23.1 25.6 27.0 31.8 36.4 35.6 35.2 29.6 26.2 24.4 25.2 26.0 30.2 31.7 13.5
Ta,
c.
70 22.9
T,
O
6.
31.5 14.6
28.4 12.7
13.9 19.0 19.5 23.0 24.6 26.8 31.7 36.5 35.6 35.1 29.4 26.0 24.0 24.9 26.0 30.0 31.5 13.2 27.8 12.4
Or it may be used in determining the humidity from the humidity charts ordinarily used, where H'
=
absolute humidity of adiabatically saturated air at Tw
H C,,
= absolute humidity of air stream
C,,
=
=
mean specific heat of air at constant pressure between T and T , mean s ecific heat of water vapor at constant pressure getween T and T, TESTS ON FOUR SALT SOLUTIONS
An experimental approach to this problem was obtained by arranging a system in which the water wet-bulb, salt solution wet-bulb, and dry-bulb temperatures were determined simultaneously and under the same conditions. Three thermometers were arranged a t the end of a 6-inch circular duct through which air was forced by a centrifugal blower. The humidity of the air was controlled by steam-heated coils sprayed with steam or water, and sufficiently removed and baffled so that no unvaporized water reached the thermometers. The air velocity was maintained a t 1500-1800 feet per minute to minimize radiation effects. The water wet bulb was wet with distilled water a t the wet-bulb temperature. The solution wet bulb was wet with a solution of reagent grade salt that had been saturated a t a higher temperature than the solution wet-bulb temperature and then cooled to the solution wet-bulb temperature. Results are shown in Table I for four salt solutions. Before the solution met-bulb temperature was determined, the bulb was wetted several times and the water was allowed
Vol. 35, No. 6
INDUSTRIAL AND ENGINEERING CHEMISTRY
732
quality, n i t h the values of T , and ( T , - AT,) in better agreement as T,, is increased. The reason for this becomes apparent by reference to Figure 2. Thu.;, as the vapor pressure increases, the change in T , and ( T , - AT,,) with a change in vapor pressure becomes smaller, and the quantity T,, may be determined more accurately. I n the case of the ammonium nitrate solution, insufficient readings were taken for proof or disproof of the postulated relation although the values of ( T , - AT,) lie reasonably close to the experimental value of T,. Comparison of the heat of crystallization with the latent heat of vaporization shows that the influence of the heat of crystallization is small in its effect on the wet-bulb temperature. The heats of crystallization are in the order of 10 B. t. u. per pound of water vaporized, and the heat of vaporization is in the order of 1000 B. t. u. per pound of water vaporized. However, in general, the points neglecting this factor lie below the theoretical curve.
70 8-KCLO, SOLUTION C-KCL SOLUTION D-NaNO. SOLUTION
Figure 2.
Vapor Pressure Curves for Saturated Salt Solutions
to evaporate until free salt was present to ensure complete saturation n hen the temperature determination was made. The values of ( T , - AT,,,) were obtained from Figures 1 and 2, and were then plotted against the experimentally determined values of T , as the ordinate for the sodium nitrate, potassium chlorate, potassium chloride, and ammonium nitrate solutionr in Figure 3, DISCUSSION OF DATA
Comparison of ( T , - AT,) n i t h the simultaneously determined value of T , indicates that the correlation postulated is sitbstantially correct. The variation of ( T , - AT,) with respect to T , appears t o be independent of the drybulb tempeiature and of the actual humidity of the air. This further substantiates Equation 9, as neither quantity appears except as a difference quantity. The influence of C is to increase slightly the value of ( T , - AT,,,) in order that the heat balance be maintained. For example, the quantity (T - C) is less than r; therefore, the value of [T - ( T , - AT,)] must be less than ( T - T u ) ; and as T and T , are Sxed under a given condition of air, (Ts- AT,) must be greater by a small amount than T,. The results obtained with the various solutions, except that of the ammonium nitrate, appear to be of the same
(Ts-ATw), DEGREES CENT. Sodium nitrate
Figure 3.
(T,-AT,),
CONCLUSIONS
Experimental results seem to point to the following conclusions on the effect of the presence of soluble salts on the wet-bulb temperatures: 1. The effect of the heat of crystallization is negligible. 2. The effect of the change of latent heat of vaporization is negligible TThen produced by the presence of a soluble salt. 3. The effect of the vapor pressure lowering produced by the presence of a soluble salt is of primary importance. 4. The change in t h e wet-bulb temperature caused by the presence of a soluble salt is an increase in temperature sufficient to equalize the vapor pressure of t,he salt solution with that of pure water at the water vet-bulb temperature. 5 , A revised psychrometric formula as follows is postulated: T(“
- H)
=
(Cpa -~HC,,)IT
-
(T,
-
AT,”)]
LITERATURE CITED
(1) B a d g e r a n d M c C a b e , “ E l e m e n t s of Chemical Engineering”, l a t ed., pp. 235-46, N e w York, McGravv-Hill Book C o . , 1931. (2) Carrier, W. H., Tmns. Am. SOC.Alfech.E n g r s . , 33. 101.5, 1021 (1911). (3) Ibid., 33, 1025 (1911). (4) Lewis, W. K., I b i d . , 44, 325 (1922). Trans. Am. Inst. Chem. (5) Sherwood, T. K., and Comings, E. W., Engrs., 28, 88 (1932). (6) W a l k e r , Lewis, McAdams, a n d Gilliland, “Principles of Cheniical Engineering”, 3rd e d . , pp. 577-94, h-ew Y o r k , M c G r a w - H i l l Book Co.. 1937.
DEGREES CENT.
Potassium chlorate
(Ts-ATw), DEGREES CENT. Potassium chloride and ammonium nitrate
Relation of SIeasured Wet-Rulb Temperatures and Values Calculated from Salt Solutions
