FUNDAMENTALS OF DRY ENG AGMCULTURAL CROPS Thai: for the Degree of 5A. S. MIG-“(BAN STATE COLLEGE George L. Gailaher 1949 F'U;'Il..‘:'x?“.'T‘LI3'§£If: 0? PET u-C'v ACE ICUL'ITTFLS‘L CPOPS 13? George L. Gallahar M A Thesis submitted to tha School of Graduate Studies of Hichigan State College of Agriculture and Applied Science In partial fulfillmant of the requirement: for the degroa of ' Q C‘ Mfif" l"~ O 1;“? 0'? Eepartmont of Agricultural Engineering 1949 {I'hESKS untitled TiT‘A‘th'I‘Am 2 2:11.: :20 A-SETICUL‘IE’ITAL 0230223 by George L. Calloher l The drying oz agricultural crops is considered from the fuzlcanxontol atané point of vapor Lrossure Gifforonco. Vapor prossuro is too primary érlving force which causes t1:.9 rflovenont of moiaturo from a material. Py showing how such factors as moisturo content, temperature, and humié- lty lnfluonco the vapor pressures involved, a logical picture of drying is prosentod. In addition, a possible methoé of making drying cal- culatlons is preposed. She method is based on vapor pres~ sure difforo nco and employs an accepted formula for cal- culating tho oveyoration rate of froo aurfaco water. F3 oztondlng tho formula anfi showing how the vapor pressure («I of a material varies with 2r; ing, it is possiolo to moko drying time calculations. lho information requlrad and mothod of mu1.:ln; tna calculations are slaown. A aorios of carefully controlled eXperimonLal costs were mafia on alfalfa boy to provide data for comparison with the camoutod values. L13 resuloa of the tests and tho comparison with c0m~utad values are given. ipprovod: g\0 AC VIII 53?; L‘TZDG 1723?: I»? ’13 The author wishes to cxpreaa his appre- oiation for the helpful suggestions and vald noble assistance of Professor D. E. Eiant of tho Department of Agricultural Engineering or flichig State College. Acknowledgement is also one tho J. I. Case Company of Racine, Eiaconain for pro- viding the funds for conducting the included experimental work. Robert u. Klein and Allan H. Gillette, students in Agricultural Engineering at Eichignn State College, gave considerable assistance in carrying out the czporimontal teats. C}. c? ,1 I, -‘.‘~" .‘c f. {46 a): $90 “‘1’ m? " " "‘ “‘1‘ C 3‘7??? mm" l-‘Li-I‘Moa U4 - L! on,” 5...... Izq'jrff GDI‘ICfIQN ----C-’—---‘---------‘-----“-------------. cfinition of the Froblem -----------------—--~~--~ mportanco of the Problem ------------------------- Previous Invcetigationa --«-~~---—-------~--~~~---— robbed of Attacking the Problem ~-------------«---- “““ PLAfifimIDV 3m? fi-Y: HG C--d--uc---------~---0---“---‘---- Types of fioisture to be Removed ------------------- Law of Evaporation -----¢------~~----¢~-----~----—- Drying fiato Expression ---------------------------- Drying Kata Preportionali 3y Factor ~---~---—-—---~- AnaIOgy Between Flow of ”oicturo, Peat Tlow, and Flow of Electricity ------------------------- 'PEFI FPEP'" {3'7}? ’nzrc (‘Ifl'fim ------‘---Q---‘---¢-‘----------- Eescription .------------------------------------.- Construction of the Chart ~---------—------------~- Hethoéa of Locating a Point on the Chart ---~------ Use of tho Page or" metric Chart --------—----------- M". A arr-'2‘ 9r .1”? “2}? -" 1:“? ‘DE? 11' L‘- J L- n: “ ‘- ‘ v17 4”... 3 -'A-.';1.J..x._-J.; l x A; I. . .s: r .v«._-. :33 O? ‘v’AS'EIDViT “"13"."5”3"I'5 lh'l :‘IS Dirac: 3'0 w..Od of Iteaflurini‘: ‘13:)01‘ Prfissuf‘e 00------- Indirac t D9 t‘erlnfi £10!) 0‘ V&' 2301‘ Irasaux‘e O---¢oou-- Change in v'apor Prcasure as Drying :ro5reasag ----- TE'MY‘} OTJE'qus’ICS C)? I}?YIT;Q -----o¢--unuooucououcoounuounnn fiotermination of Heat of Adsorption ~------------- C0113 L631 :1 '6 t 91111:) Procaflfl ..-------------C--------- I'Lfflcioncz'y of 13.35:; {13' oan-no«I.--anon-ocuncao-------0--- E'XP: m :3 TAL PROCL-E’T'T’ :3 a-..coo—u---nun-acnaanuonocao“cnno rtdicr‘T‘? T'Ijz‘z \T' '1’? : 1‘1;'3il‘\1"’flt T1353 ---w--~ucunuuonoaoucunocu--- r803; '18 Of (4113 ‘:quipmnt -c¢-----o-oo-a--uounarc-o--- T'0881.P1I'!g and cont”01 DOVlcoa “can---------------- t-Jara ti B‘QVLCQS O---—---~-----------uc-oo“on-uccoa- yr“ ryqun‘ 1p. C‘ "‘T“"‘ ’ '5'! ‘ ' ';.'i-‘ 1" 5 u... I +'_ 1 -Q--------‘--‘------‘—------‘---------- 32 36 37 :59 47 43 57 59 61 111 ‘ m ~- ray" "1"» fl .0: w a- w NWN “ W? 4.3 IECIIE‘, E IUH Or ,, 13;, T1: “,5 zv‘htfs u-.-u--onoa--o-uaoum¢um Agreement of Data and Thnory --------—--~-...-- IflflUEHC 0 Of T623para turfi “co--m-cnoooauon.-- Influeno 0 of Humid: ty Ouwuqonnuannuouancwau Erreo t or r’epth -muoc‘cnonoanwuc -u-QucauO-nou- Influence Of A1? F10“ ..--...---..-fl---‘--‘..‘.. Effec 1', 01‘ [ans 1 ty ”nuuudam-”cucnumcw 8 Of 33:8 t8 P131 "Co-u----ononnnncunanuouaaud "013 ture content ‘-‘“”‘--“-Q-”W--Q-Qm-" CDHCLUSI‘flS fiooonu-a---acununucono---oooonoacnans-no. 1v TAB LT'ZS Pegs inble 1 Vapor Pressure of Hard Bad winter Whaat at 80 it. ““-'--0‘--I-da‘”--—¢-----“u-__ 28 Table 2 Illustrative Calculation: for Vapor Pressure _ Table 3 Vapor Pressure of Alfalfa .....-........... 34 ?fibla 4 method of Camputing Brying Tina for*¥heat - 42 Table 5 Computation: for Laavlng Vapor Pranauro'~- 42 Table 6 Drying Tima for Second Layer -«-~ 45 Thblo 7 Summary of Tests .......-..-...------..--.. 67 Table 5 Bate framiDrying Tests ...--...----..--...- 68 Thblo 9 Computations for Drying Tfista ....-.......- 71 Figure Figure 2 Figure 3 Figure 4 Figure Figure ?igure Figure Figure Figure Figure Figure Eigure I’i aura Figure Figure Figure Figure E’igure ' £1! 10 11 13 14 ”Tr"??? " ‘ AUU.A‘- PeyohrOmotric Chart for Eerometrio Freesure of 29.92 ”Hg. -....-..-..-.... Construction of the Fayehrouetric Chart . Apparatus for Measuring Vapor Pressure - Equilibrium.moioture Content Curve for flora fled.%inter about at 80°F. ........ Vopor Pressure of Hard Red Winter uneat at 8002?. ma‘mflm-”OQ“--~m Vapor Preeaure of Hard Red winter Wheat at Various Tomgeratm'eg macaw-m Log-Log Plot of Altair: Vapor Pressure - Variation of Heat of Adsorption with moisture Contentrbr Alfalfa .......--.. Illustrative Curve of Drying flute Reciprocal vs yoiaturo Content ........ Typical Drying Time Curve ............... Drying Curves for Several Layers Sketch of Laboratory Drying Apparatus ... General View of Apparatus from.?en End - Conerei View 0: Apparatus from Plenum 3m Wanwmmwumanquwwww 0108 eup or Fan u“--------hmfifl--'"--“ Steam Inlet for Humidifying the Air ..... 1:190 trlc 393.66? C0113 m-auaamum Control Eectio 398193 and Plonm WMOOG“QW Drlfioa and flit Air £38513}ny ““W Page 14 16 23 26 (.1 O u 01 (a U: Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure v1 Air Compressor and Supply .....-...-..... Monometero ......-----........-....-.---- Control Apparatus .......--..-.---..-.... Squeezing 3316 into Test Section --¢-- Efioighing the Bale --«-«-m~.m----~ Bale Removed fromgTest Section -.¢.¢00-oo Vapor Pressure of Alfalfa for the Er’y ins Te 8 t‘ Won-mono“ .. Comparison of Computed Curves with Test I} a t B acmonmoumnomn-ndam Comparison of Computed Curves with Test 33‘ a t a mun-Nb“ mnwucuduwoonnwouoecuu Comporiaon or Computed Curves with Test pa ta ”“‘-----”- anon-puma...“ Page 57 58 61 62 64 70 72 73 74 O on 'u K! K” vii S " '35:?"- 3L3 drying rate, lbs of rater/hour proportionality factor, lbs of water/(hour)(ft2)("ng) vapor pressure of water, either free or in a connooity, "Kg vapor pressure or water in the air. ”E3 water nurfaoe area, ftg experimental oonetentn velocity, rt/nin drying rate, fob/hour prOportionnlity factor. finb/Xhour)(“fig) instrumental constant in payehrometry: equals approximately 3.67 barometric pressure. "Hg dry'bulb temperature, °F vet bulb temperature, °P moisture content, fi'dry'basin (fob) time, hours eXperimentel factor: equall approximately 1.45 for'balea of alfalfa hey ro ortionnlity factor: equal- C' times 1b dry air/ fhr (lb dry matter) IKTS??UCTIQH Definition of the Problem The problem undertaken in this thesis is to explain what causes drying and to show how temperature, humidity, air flow, moisture content, and density influence the drying of agricultural crepe. Importance of the Problem The proper drying of crops such as hay and grain is an important problem in agriculture today. The method of natural field drying which has been depended upon for con- turiee is no longer practical. Too much food value is lost when the crap is dried in the field exposed to the elements or nature. The longer the drying time, the more losses sustained. Therefore, faster drying by artificial means is desirable. However, the current artificial drying practices are not based on well founded principles, but rather on a fee miscellaneous rules-of-the-thunb. If the real benefits of artificial drying are to be achieved, a fundamental understanding of the drying process and the variables in- volved in drying is necessary. eith such information, artificial drying williresult in high quality products and economy of Operation.f/ _Previous Investigations fibers were a few neagor attempts at artificial drying of grains made during/the 19th century. Not until the close of the century, however, was artificial drying being used with any real success; and than it was with such.commcditiea as prunes, raisins, and walnuts. Between 1900 and 1925 the first recorded attempts to dry forage craps were made. Dur- ing this period several drying plants were constructed, one by the Cnited States Department of Agriculture at Hsyts, Nissouri in 1910. Since 1925, artificial drying of agricultural crOps was undertaken in earnest. Today, the literature is full of reports on artificial drying eXperiences. A complete bibliography on agricultural drying for the past 25 years will contain several hundred papers. The papers are notice- ably lacking, however, in that they do not supply the fundamentals of drying necessary to set up and solve the drying problems of agriculture. They do not contain complete information so that they can be correlated with the work of others. ihe fundamentals and design facts which are common to all drying problems have not been determined. In late years the need for this type of information has been recognized and strides in this direction are being made. Some of the more notable work along this line are investigations by Barrel, Fentonz, and Hukills. Their investigations have supplied some of the basic drying information as applied to agriculture. For the truly theoretical approach to drying, the chem- ical engineers have made the biggest contribution. Work by Lewis4, Sherwoods, and Newman6 has provided the most funda- mental picture of the drying process. A better under- standing of their work will do much to solve the drying problems as applied to agriculture. a. H. Carrier of air conditioning and refrigeration fame also has contributed considerable basic information to the drying field. He has 7.8 written several important papers and is an authority on the subject. Method of Attacking the Problem An extensive review of the important drying literature was made. The purpose was to start with the fundamentals of the drying problem and find out exactly "what causes a commodity to dry". It was felt that the theory of drying should be understood before any experimental work was started. As a result, the first part of the thesis is theoretical and explains the drying problem from the funda- mental standpoint of vapor pressure difference. Vapor pressure is the primary driving force which causes movement of moisture from.a substance. By showing how such factors as moisture content, temperature, and humidity influence the vapor pressures involved, one can gain a logical picture of drying. In addition, a possible method of making drying calcu- lations is proposed. The method is based on vapor pressure difference and employs an accepted formula8 for calculating the evaporation rate of free surface water. By extending the formula and showing how the vapor pressure of a commodity varies with drying, it is possible to make drying time calculations. The information required and method of making such calculations are shown. In order to substantiate the theoretical calculations, a series of carefully controlled experimental tests were made. These tests were conducted on alfalfa hay and the results of this work comprise the last part of this thesis. EXPLAEATIOH OF DRYING Types of Moisture to be Removed Agricultural commodities may be termed hygroscOpic materials because they contain varying amount of hygros- copic water. They may also contain free moisture, especially when their moisture content is very high. These two types of moisture make up the total moisture contents. Free moisture is any water that is readily evaporated and is not held in the liquid state by any forces other than those normally found for an exposed surface of water. Such moisture exerts a vapor pressure according to its tempera- ture. A film or drOplets of water on a leaf might be considered free moisture. HygroscOpic moisture is that moisture which is held internally in a substance. In this condition it is held more firmly than is free moisture. Its vapor pressure is reduced below that of free moisture by the absorptive effect of the substanceV. A definite value of moisture content is the demarcation line between the two kinds of moisture. All in excess of this value is free moisture. Under natural conditions free moisture will rapidly evaporate leaving only the hygroscOpic water. Some of the hygroscopic moisture will then also evaporate until the commodity reaches what is called equilibrium with the surrounding air. Generally days and even weeks are required to reach equilibrium. The amount of hygroscOpic water in a material which is in equilibrium with the surrounding air depends on the relative humidity of the air. The greater the relative humidity, the more hygroscopic moisture. (Also, the air temperature influences the equilibrium but in a slight amount. With other things constant, lower air temperature means more hygroscOpic moisture.) If the relative humidity is held at zero, all the hygroscopic moisture will leave the substance (gradually) and the result will be equivalent to an oven dry substance. On the other hand if the relative humidity is raised to 100%, the substance will pick up additional water from.the air and reach a maximum value of hygroscOpic moisture. This value is also the previously mentioned dividing line. If any more moisture is added to the sub— stance it will be free moisture. Law of Evaporation Drying is the removal of any evaporate liquid. In this work, the term drying is used to denote the evaporation of water from a farm commodity such as hay or grain. This water in the form of a vapor then dissipates into the surrounding air. All such evaporation processes when involving free water are governed by the law of evaporation: For a given condition of atmospheric move- ment, the rate of evaporation is preportional to the difference in vapor pressure between the liquid and the vapor of that liquid in the immediate vicinity (see page 1694 of reference 9). In theoretical considerations water vapor is treated as a perfect gas. This makes it amenable to mathematical computations. As a gas, it is easy to understand that the vapor will tend to flow from a region of high pressure to one of lower pressure. This is the primary factor that causes the flow of water vapor. The above law states this clearly and furthermore says that the rate of flow is proportional to the vapor pressure difference. With such a law many moisture flow problems may be understood quite simply if the vapor pressures involved are known. Drying Rate Expression The rate of evaporation of free moisture follows the law of evaporation and is fairly well understood. It depends on (1) the vapor pressure of the moisture which is a function of its temperature, (2) the vapor pressure of the surrounding air, and (5) the effective velocity of the surrounding air. These factors may be expressed in the following relationship which is the law of evaporation stated as a formula: it" - K' A (p - pa) (1) where W' equals pounds of water per hour, A is the surface area, p is the vapor pressure of the liquid water, pa is the vapor pressure of the moisture in the air, and K' is the preportionality factor which includes the effect of velocity. For air blowing over a free water surface K' has been found equal to a +‘bV where V is the air velocity and a and.b are experimental constants depending upon the direction of air flowg. Equation (1) may be considered the maximum rate of dry- ing attainable for any substance. In practice only the initial stages of drying of very thin materials attain this. In hygroscOpic materials, as the surface free moisture is evaporated the rate of drying decreases. However, Carrierv states that if the reduced vapor pressure of the material (below that of free moisture) is known, the expression will still be valid. In other words the drying rate remains the same function of the vapor pressure difference, the reduced drying rate being accounted for by the reduced value of p. Such a statement appears reasonably correct. The difference in vapor pressure has long been considered the primary function affecting drying. Whether or not the preportion- ality factor remains constant throughout the whole drying process, however, is a point not clear. Since use of equation 1 requires a value for K' and it is so important in moisture flow considerations, the next section discusses K' in detail. Frying hate Proportionality Factor ihe preportionality factor K' of the drying rate expression must be detersined from experimental data. Very complete information is required before t can be evaluated. Because such data are limited, values of K! are not readily available. Every material will have its own value and in addition it may vary somewhat as drying progresses. Earre indicates some variation, in his work with vapor pressures.1 Any such variation, if found, may be due to the "velocity effect". khan a substance is quite wet the drying rate 10 varies semowhat with velocity , while at low moisture 11 contents the velocity has no appreciable effect. Some apparent variation. however, may be due only to added heat by radiation or conduction10 which is difficult to account for. The chances are that if a curate vapor pressure information is available the variation in K' with drying will be found quite slight. The reduced difference in vapor pressure with drying provides a logical means of accounting for reduced drying rate. For the present, since any variation large or small is not actually known, K' will be assumed a constant. Kethods of handling it as a variable can be in: duced if experimental evidence warrants. another problem.cncountered with the preportionality factor is the units involved. ?or evaporation from a water surface, pounds of water per hour per unit vapor pressure difference per square foot of surface is reasonable. For 4.10- drying a commodity such as hay or grain, however, a surface area is rather difficult to conceive. Since the surface area is roughly preportional to the dry weight, "pounds of dry matter" in place of "square foot of surface" should be suit- able. With this change, the drying rate is in lb of water/ (lb dry matter)(hr). If this is multiplied by 100 the drying rate will be change in moisture content (fidb) per hour. Since the moisture content is the desired value in agricul- tural work it is convenient to include the factor "100". ihe drying rate expression now becomes: a - K (p - pa) (2) where p and pa are defined as before; K is change in moisture content (fidb)/(hour)("fig), and W is change in moisture content (flfib) per hour. Analogy Between Flow of hoisture, Heat Flow, and Flow of Electricity It is interesting to note that a direct analogy exists between the flow of water vapor, heat flow, and the flow of electricity. In heat conduction problems, the flow of heat Q (in Btu/hr) equals the thermal conductivity times the cross-sectional area taken normal to the heat flow times dt/dL. there dt/dL is the change in temperature with distance through which the heat must flow. This temperature difference is the driving force that causes the heat to flow: Q a thermal conductivity x Area x %E (3) a ll - In electrical problems, the flow of current I (in amperes or coulombs/sec) equals the electrical conductivity times the cross-sectional area taken normal to the current flow times dE/dL. there dE/dL is the drOp in voltage with distance through which the current must flow. ihis voltage difference is the driving force that causes current to flow: I 8 electrical conductivity x Area x g% (4) Likewise in vapor problems, the flow of water vapor V (in pounds/hr) equals the permeability times the cross- sectional area taken normal to the moisture flow times 2 there dp/dL is the change in vapor pressure with dp/dL.1 distance through which the vapor must flow. ihis pressure difference is the driving force that causes the vapor to flow: t 8 permeability x Area x fig. (5) The above flow equations are well established for heat flow and current flow. Experimental values of thernal and electrical conductivities have been obtained for many materials. Experience has shown the equations to be quite accurate and valuable. ihe vapor flow equation is not so well established, however. Experimental values of perme- ‘ability for various materials are not too well known. The” expression for vapor flow is relatively new. In recent years, interest in permeability has increased with the demand for vapor barriers for insulation and packaging of foods. A wrapper with a low permeance is considered very good because it greatly retards the flow of -13.. water vapor through it. She distinction between permeance and permeability is important and is similar to that between conduction and conductivity. Permeance is the rate of water vapor transmission through any specified thickness of material while permeability indicates rate per unit thickness. The permeance of an inch board is much smaller than the permeance of a shaving cut from it, yet their permeabilities are the same. Description A study of moisture and its removal will involve a know- ledge of air, moisture, and their mixtures. An understanding of the psychrometric chart provides most of this information. It presents the preperties of air-moisture mixtures in a convenient form and is a valuable key to investigating moisture problems. One disadvantage of the chart is that it applies for only one value of barometric pressure. For air or convection drying of farm crepe, however, standard barometric pressure provides sufficient accuracy. The usual form of the psychrometric chart is shown in figure 1. ihe bottom scale is the dry bulb temperature of the air in question. The vertical scale on the left is the vapor pressure of the moisture in the air. The vertical scale on the right is the absolute humidity of the air in grains of moisture per pound of dry air. The curves slanting up to the right are lines of relative humidity in percent. She lines slanting down to the right are constant wet bulb temperatures. It can be seen that the important properties of air are clearly represented. Construction of the Chart The information on the psychrometric chart has been computed originally from algebraic formulas. In certain instances it may be desirable to compute the required If, )4 e F‘- Q q. a «a e a ‘ ~a Pr V0? 73!" I {" s a.) I \ £-_: ') qu Edit Tfrflp‘pt‘iszY‘e {:53} Figure; |.—- Fgrgchrcmetric Churt f;,,~ Em‘cnistric PFESSUYE? (if 23.32. ”H94. a _ ‘ um: .51.»; t. \ rt ‘U’ C J t ,4 <2“ I information directly. Because of this reason and the importance of the psychromctric chart in drying, the theory and construction of it are given. The theory involved in its construction is only approximate but for practical pur- poses the chart is very useful and satisfactory. (Kore accurate air-vapor prepertics will soon be available for extremely critical scientific work. the American Society for Heating and Ventilating Engineers is sponsoring a complete reevaluation of airvvapor prepertics.13) The first step in constructing a psychr metric chart is establishment of a pressure-temperature curve for saturated water. Such values are available in any steam tsbles.14 Figure Ea shows this curve. Everyone is acquainted with one point on this curve which is the boiling point of water at standard pressure, 212°? at 14.7 psi. The normal psychro- metric chart uses only the lower part of this curve for the air temperatures encountered are generally in the 35-1100? range. The water vaoor saturation pressures in this range are quite small so that it is more convenient to give pressure in inches of mercury ("Hg . Ibis curve is the saturation or 100$ relative humidity line seen on all psychro- metric charts. by definition, relative humidity is the ratio of th actual vapor pressure to the pressure of saturated vapor at t the prevailing dry bulb temperature, d. Therefore, the relative humidity lines may be quickly established once the saturation curve is drawn. for example the SOJ curve is a II;16 II :00 joo . :1 J av J «J L A «.L O 1'. If my; V rapivns 1.an LCQG> 1 L J I _ b b b h .‘J .L., A," 5 O 5 o .4. n... x; .0. I to. o) ?rratur€ “Ten. ,fl:«rn r9 fl 50 ‘C Q “3 ,d ‘ 70 DH.) BAIL: Tfiw-r‘Pt'tnt aye a" co Mo ED 9G 70 so DV1 53 I, r\ r, F‘t '. ‘ ‘1 .I.) \. BU Us TE W"?c-‘Y‘_)\{ ‘A‘f ;: (a) iflfitLriC n1 9{:}1V: S P traction J, .2 C on Chart ~17- line drawn through.pointa at each value of temperature that are 50% or the vertical distance up to the saturation pressure. Figure 2b shows the relative humidity lines at increments of 25;. In.mmny psyohrometrio charts the vapor pressure ordinate scale in not given and instead the absolute humidity is shown. Absolute humidity in pounds or grains or moisture/ pound of dry air. The relationship between these two scale: may be determinod from the perfect gel law for mixtures. P V r R T xm’mxxm (6) where P in pressure in Ib/Tte, V is total volume in fts, m.ie pound: of gas, R in the gas eonutent and T in absolute temperature in degree: Rankine. The subscript m,ia for the mixture and x for one or the gases making up the mixture. The mixture in.thia cane is that of dry air and water vapor. Let the subscript v represent the water vapor and a the dry air. ?hen (6) may'be written for vapor and air as: P'Zh_:tn§fi;gn (7) and 1’ ‘Va : 333.?“ (5) Equation (7) may be divided by equation (8) giving: P m.R *‘n Ff-g_f§f-i: 1.61 (9) According to Bolton's law or partial pressures P, + P‘ 3 B or barometric pressure. Thus equation (9) may be written as: P m J ‘v ma Lot ma equal one pound of dry air and solve for mv (lb vspor/ lb dry air): m - Pv (11) V ’ 1.cl(s - PVT If D and Pv are in "fig, and mv is in grains of moisture the above expression will reouce to rev equals approximately 150 Pv for values of Pv up to about l”Hg. Figure 2c includes the absolute humidity scale as established from this relation- ship. Another value given on most psy hronetric charts is the wet bulb temperature, t'. This is the temperature of s therndmeter whose bulb is covered with an absorbent material saturated with water. For accurate readings the air must be moving past the thermometer at a velocity of 10 ft/sec or greater. There are two theories involving the wet bulb tempera- ture. One is the diffusional theory of Yexwoll and the other r loolsims that is the convectionsl theory of August. Arnold the true wet bulb temperature depends on both. In its simplest form, the relationship involving the wet bulb 16 temperature is: -4 p - pa : C B (td - tw) 10 (12) where p equals the water vapor pressure at the wet bulb temperature, C is an instrumental constant, sné the remaining 1a- - v fl terms have been previously defined. The value of C is where the theories differ. The United States leather Bureau uses 17 This variation a value of C which varies slightly with tw' was determined from a large series of eXperiments by Professor Ferrel. For ordinary work, when temperatures are in OF and pressures in "H3, C may be used as 3.57. tith this value, equation (12) can be used to construct constant set bulb temperature lines. Figure 2d shows the psychrometrie chart with the wet bulb temperature lines added. Methods of Locating a Point on the Chart Any given air sample is represented by some one point on the chart. Gnce the point is located, the various properties of the sample, such as humidity, vapor pressure, etc. can be read directly. There are many methods of locating a point on the psychrometric chart, but three are more common. 1- The QEEMEEEEE method is probably the most accurate method. Ry definition, the dew point is the temperature at which the air—vapor mixture becomes saturated by cooling at constant pressure. ihis temperature on the 100$ relative humidity curve gives the vapor pressure. ins intersection of the dry bulb temperature and the vapor pressure locates the point in question. 2- Use of £93 and £131 M temperatures is a very common method of entering the psychrometric chart. A sling psychrometer provides an easy method of getting these temperatures. The intersection of these two temperature lines locates the desired point on the chart. 3- The hair hygrometer measures the relative humidity directly. It is not too accurate unless frequently calibrated but is all right for some purposes. If the air temperature is also known that air can be found on the chart. Use or the Psychrometric Chart All the various processes of cooling or heating and dry- ing or humidifying the air can be followed on the psychro- metric chart. Since the drying generally practiced with agricultural products is convection or air drying, the chart is very useful in solving drying problems. As mentioned in a previous section the drying rate is dependent on the vapor pressure of the air. ibis can be read quickly from the chart for any air. fishy other things can be included on the psychrometric chart such as Specific volume, sensible heat factor, total heat of the air, etc. Some of the more common changes that occur to air can quickly be shown. For example, consider air at point C on the chart in figure 1. If this air is heated it follows a horizontal line to the right from C.K'Cooling of the air follows a horizontal line to the left from C. As the air is cooled its relative humidity increases. The temperature at which relative humidity reaches 100$ is the dew point temperature. If it is cooled still further some of the moisture will condense out and the vapor pressure will be lowered. Anotherlmethod of removing moisture is to pass the air through.an adsorber such as silica gel. Such a process follows a path downward and to the right from point C. The air is heated because the heat or vaporization is released whenymoisture is condensed out of the air, The total heat content or enthalpy of the air will be mentioned because it is important in drying processes. The total heat content is the summation of the latent heat (due to change in state) and the sensible heat (due to change in temperature). The total heat content has been found to be almost constant along the wet bulb temperature lines. Because of this, many psychrometric charts have the wet bulb temperature lines labeled in Btu/lb. Actually this value is the sigma heat as defined by Carrier18 but the total heat is practically the came. The total heat value is useful in determining how many Btu are required for a certain process. ERAS Eff-KEIIT 037'“ VAPDH PET-$313138 OF“ VARIOUS COEQZDDITIEQ’S Direct hethod of heasuring Vapor Pressures There are several methods of measuring the vapor pressure of a commodity. A direct method which is actually very simple but which requires good equipment and careful work is described herein. A rough sketch of the necessary apparatus is shown in figure 5. A is the flask which contains the material - for example, a handful of wheat - the vapor pressure of which is desired. T is a U-shaped section of glass tubing called a trap. A manometer of some form is necessary for measuring the pressure and is shown in the figure. C and D are stepcocks. Ground glass Joints should be used to insure tight fits. The manometrio fluid can be either mercury or an oil of low vapor pressure. The oil provides greater sensitivity but requires more care in using. A mercury manometer of the Dubrovin type is very desirable, if available. It has a sensitivity about seven times that of an ordinary U-tube mercury manometer. Reference 19 gives a complete description of some extremely accurate vapor pressure measuring apparatus. The procedure for making a measurement is as follows: The material for which the vapor pressure is desired is placed in flask A and the flask is then surrounded by a constant temperature bath. The flask containing the sample and th rest of the apparatus are evacuated through the Open stopcocks I \ \ N '~._ '1 f A ‘1 F h\ 71 t ‘- ~53 . t _ \ ' L ’\ ‘\ m. /' Q- W \A /--~. /‘ N" J N. \/ bf‘\- 21\' [I K _. J L‘\‘_"‘: \ / ma- " ”’1 ' ’7 P1“. + \‘N . 4 u \ —... \-__ “ w. ’/ Ex‘ ' L 9-.“ W “ .. ‘ “\‘j , \x.\. _// K '\"1 x -_ 1 \‘1 “. F‘- . L '- " (.1: A" I ’ r:*/,r Mahometcr I" 7- .. ‘ k h‘ \ ‘ . u \ \ ‘s O . ' I ‘ a Figure 3. - Apparatus For Measur'mg Vapor Pressure. - 24 - C and D with an oil pump. During the evacuation trap i’is kept cold by means of a solid carbon dioxide-alcohol mixture. This causes the water vapor to freeze in the trap while the noncondensible gasses (air er carbon dioxide) are exhausted. when the equipment is evacuated, stOpcock D is closed and the small amount of ice in the trap is allowed to evaporate. It may require a half hour or more for the vapor pressure in the equipment to reach equilibrium with the sample. This pressure can then be read on the manometer and is the vapor pressure of the commodity. its total time per test should not take over an hour. ihis method can be used to determine the vapor pressure of many materials and also the vapor pressure of the air samples. Indirect Determination of Vapor Pressure ?hen a hygroscopic substance is placed in an atmosphere of constant humidity, its moisture content gradually changes until it reaches and maintains a definite value depending upon the air humidity. This is called the equilibrium moisture content. Equilibrium moisture contents have been established experimentally for many materials in atmospheres of various temperatures and relative humidities. A common method or obtaining air with a definite relative humidity is with sulfuric acid solutions.20 The more concentrated the acid, the less moisture in the air above it. Samples can be suspended in jars over acid soluo tions of different strengths. By weighing the samples at 1‘3 (.3 C intervals and finding the equilibrium weights, the equilibrium moisture content can be determined. Reference 21 tells of such tests for alfalfa hay. Such tests generally take several weeks. An illustrative equilibrium moisture content curve for hard red winter wheat22 is shown in figure 4. Such curves are generally established for a certain temperature. (Figure 4 is for 80°F.) A family of similar curves exists for other temperatures. The actual difference in the curves for 10-200? variation, however, has generally been found to be quite slight. Such equilibrium.moisture content information is quite valuable and may be used to determine the vapor pressure of the given commodity. Barre makes this suggestion as an aid in understanding moisture transfer problems. Fenton determined vapor pressures from such equilibrium information and plotted the results directly on the psychrometric chart.2 Another method of handling the vapor pressure is to plot it against the moisture content, making separate curves for each temperature. The mechanics of this Operation are quite simple. Consider the curve of figure 4 which gives the equilibrium.moisture content for wheat in air at various relative humidities and 80°F. Since the moisture content of the wheat is in equilibrium with the moisture in the air, the vapor pressure of the moisture in the wheat must equal the vapor pressure of the air. (If the vapor pressures are unequal, moisture will be transferred and the wheat will not be in equilibrium.) ihe vapor pressure of the air is readily .. m. .0. u 9... p n w +3 .i u u. _. .. ..2 ! .. . I ..v near. We whivflmmug annex, l.m. ebsmi 3....5 test 0 meta: as om om oi L“ a. C) mp. »~. _ a ‘\o w (l ‘ . ....J u t If.u my: hLSI LOW waiju pimuCoU f.\ ‘1) /’ ... ) "-y. '-> I creases; ezeiei23smw 1.4u maje_u ..... Asc.msle:cs: e>:s:c Om mm 0 #1 i _ . _ \n h . . i _ \ i m we \ n . . \ . m \\ n .3: T _ .\. , 4. it!) . o h u.‘t. \\ . ‘\.\ ii. p \\.\x _ . \\ h \\ \e. ‘ ..\ u A .\ \ v\x. H m . . . i H 4 i . . relllxtnrgll .1 6 b i . n. o. om om C) 5.0 1:140 j j 3a" . .' ’ J D g i ‘ o ' .27.. determined from.the psychrometric chart for the given humidity and the 80°F dry bulb temperaturb. This vapor pressure is that of the wheat at that moisture content and at 80°F. Table 1 presents an easy manner of calculating the vapor \ pressures for various moisture contents. ihe first two columns are arbitrary points taken from the data used for figure 4. Notice that the moisture contentfis-axpressed on a dry basis. The dry basis facilitates comparison and is considered the best method by most investigators. \The first value in the vapor pressure column is the saturation vapor pressure at 80°F. The remaining values in the column are simply the first value multiplied by the corresponding relative humidity as a decimal. The resulting vapor pressure curve is shown in figure 5. Its height is limited by the maximum.vapor pressure in the table. If the moisture content is increased, the vapor pressure curve remains level. This is the vapor pressure of free moisture and it can not go any higher for this temperature. All moisture above the 34% value is of course free moisture. The reduction of the vapor pressure, as the moisture content decreases (due to absorptive effect of the material), is readily seen. In all probability this curve goes to the origin as indicated by the dotted line. It is hard to visualize water that does not exert at least some small vapor pressure. The curve, there- fore, is quite well defined and can be a big help in under- standing the process of drying. - - v v , r t - « x v - -. v 1 ~ ~ 7 . 7 o. , . ~ » 7 v' — . . . r - ‘ .‘I - ’ '7 I ' » . \ ‘ < n ' .. . A I ._. J. O b - i . W I . “A ‘ - A l . ‘ A . A , v _ - . - 4 u . p - ~ . . ' * "‘ + 1' 7". ; F" i C: ’ l ""j V v. / .fl .1 L _ ~.V‘ .g. ,' K. L ‘s v4 ~ . \7: , '1 . - . + '”..‘...' 3? < ~. in -_ (3% a 4' r . ."h“‘ QV-Pv;. \J A - \4 A ‘ U ~ x ‘ .s . h V ~J A a ' 5 _ 9‘ . ‘ l . . i. I V x. \ ,I ' ‘. f .’ , .. f i , I ‘ I a J . ~ ‘ - h--.;O— n-‘w~—aj’ .s—’ ”mun > _ -u “—v -.-~O.. a. “BOA-Mfinq-mv-g- ' r'- - r‘. A 1 ' ' l (a j I . . . - 1.‘ 3 v u ... ." a. - O ‘ L, .' , P . - l -‘ . .- _I ._ . i L - ,p L. a. . l c ' 1 'fi 3 "v - ~ - 1 “L. ’ Q .5. j — rfi p (‘ ‘. I 5 ‘I- ' ‘I ' r . ‘ I. f U \z' .’ . by "v 1 z- [,4 ’5 ,4 '_,' l J 9 ‘- - ' " a 1 r“. "i 7 fl 7 ‘ e w - x. .1 . ~ i A '-‘ -‘ "- ~ ‘ , \ , ' r". ( " -5. ‘ O .1 v 1 . A" T r -' 'Y‘ ~" ' - ‘ ‘V' ‘ N a ‘ vy~v7 y (v- ;\‘- . r r' . v o » v— - r {11.4 ... ‘ l -) . ' ‘ ' i“ _ . . A . J . n . a4 a A A . . _ . » _ r7, . 1-» . .- 1 y - T y ' ‘ u -. . ‘ ‘i. y . '. i I 1" 1 1 . ,, ,, - I .‘v -,. - A‘V . ' -' ) - Y z T- ‘ 9. U‘ * '. ' ._. ,, \ v V . a g ‘4 I s l‘ ‘ ‘f‘ 1. - V 4 ~ . A - s" y-. w ‘. s. ',' 'h ' ;' x .f- "‘ I ._ v .} ..\ A - I 4 u . I ‘ . . v |_ . . - I A » J ~1v ; 4_ x. g A . '1 ' 1'} i “ " ' vs: V ’ 'L ' V . A . at “.“w... . \, r_‘ ‘- , o s. .‘ . r. -- . I “q l . . ’ ’ ‘ ;~, I4 .~ ' k, 1 f. ‘ ‘ l .- _ —. A ‘ "I ' so ‘ ‘I .n . “0"“.-- r a 1 _- 0 ‘1 .L . .1 g . ,. d ~\ >“‘ a ‘ ’ r . . . - |‘ 1 : ‘ r" ‘«.V‘ "* . T"\' -;.) a l I 3 4‘ . ‘ . A .A ,4 .. . \I” \/’ -. ' - ‘ , . . .-\ I ‘ v—\ ”5 1" 9 V\ .' ‘ \ .A - J A - (.1 .1 ’ p.’ ‘ — - .. \ “ -4w«-,;_.rv rump. 1‘,” ‘3 -~( . ‘, Q_ _ LL . ' fl 4 rd . L .o‘ .z a j .- ‘ \ ' ow...-— -4.— '~ ' t. - 4. . A ‘ F .3 ' I - i. . - .t 1'} ‘ J , V .. - K J' . . . ‘ .L \ _'_‘ ___, -.*~. u“, ~,....__,-4.. a-......'..- .. .._... .i ,, . , . .-,.. , .._... -... . -_.— _« ~—-'"‘— ~-. ; ,1 7 .- ed - . ' L ' ‘v ’- - I '. \ C -' "r i -‘ 3' 3. , q IV, -/ ‘ . - I” ‘ I -, .. - x In 7‘ . o— r- 1 ‘ . i ‘I H, .a a. D ._ A. . ' A" 7 , ,. s~ ‘ - ,0 '\ l I i . J- . -L- -1 a ' i Q ,4. It is interesting to see what the vapor pressure curves are like for this same winter wheat at other temperatures. By assuming the given curve in figure 4 to be reasonably correct for other temperatures within lO-2OOF, new vapor pressure curves can be quickly calculated. This is done by adding another vapor pressure column to table 1 for the new temperature. Figure 6 shows the vapor pressure curves for temperatures of 70, 80, 90, and lOOOF. The increase in vapor pressure with temperature is quite noticeable and is imporv tent in drying. Change in Vapor Pressure as Drying Progresses If the temperature of a commodity remained constant as drying progressed, its vapor pressure would follow a constant temperature line such as given on figure 6. Experience has shown, however, that the temperature of a substance varies as it dries. A water surface assumes the wet bulb temperature ' as it evaporates.7 Likewise, an agricultural commodity is at wet bulb temperature when it has free moisture evaporating from it. As drying progresses and hygrosQOpic water is re- moved, the temperature of the commodity rises until it reaches the dry bulb temperature at the equilibrium.moisture content. As the temperature changes, so does the vapor pressure. Carrier shows that equation 12 may be used to calculate the actual values of vapor pressure as drying progresses.7 For this use, t' is the temperature of the material which.varies from the wet bulb temperature to the dry bulb temperature and p is the vapor pressure of the material corresponding to its temperature. 2.5 Y ., . *>.m.~.-m..___m“.f nus-n. u-«M "u... -—A A““>—.‘—‘.-~ «*.H..-.. -...._,- . - Jau“. ’ I L ‘ -. ' I . K i A . I i ‘ i J a n 1 IO 20 A 30 4O Moisture Centent (9455) Figure 6.” Vapor Pressure OF Hard Red Winter Wheat at Various Temperatures. As an example, assume a drying air with ta 3 100°? and tv 3 70°? for the hard red winter sheet of figure 6. From the psychrometric chart Pa is read as .41"£g. Table 2 shows how the formula may be used. The resulting values of vapor pressure have been plotted on the curves of figure 6. The dashed line drawn threugh them represents the true value of the vapor pressure as drying pregresses. visa V Us.) - "The.“ ‘REDC’YE’ZE IC 3 0'5" TESTING East Required and Sources than agricultural crops dry, the water in them is evaporated and dispersed into the surrounding air. Great quantities of heat are required to vaporize this water. In general there are two primary sources or heat forthis pur- pose: heat in the surrounding air, and heat iron respiration processes during which dry matter is consumed. Terry says that 6800 8.33.3. are released per pound or dry matter comma.” Heat may also be conducted and radiated to the material from surrmmding warmer bodies. Craps in the field receive great quantities or radiant energy from the sun. For artificial drying, however, heat supplied by convection from the air is most important. me air may be either at the ambient temperature or higher because of some supplementary heat source. Determination of Heat of Adsorption The heat required to vaporize a unit quantity of water from a farm comedity is called the heat of adsorption. Its value is greater than the heat of vaporization for free water. The heat of vaporization can be read directly from the steam tables but the heat of adsorption is not so easily obtained. It is different for each material considered and also varies with the moisture content and temperature. Accurate values are not available and have been holding back drying research. However, if accurate values of vapor pressure are known for a substance, the heat of adsorption 24 provides can.be calculated. in equation develOped by 0thmer a convenient method. 10g p (of a heat of vaporization log p (of (15) free water) Heat of adsorptibn x material) +>C This indicates that the slepe of a log-log plot of commodity vapor pressure vs free water vapor pressure is equal to the ratio between the heat of adsorption and the heat of vapor- ization. In order to use equation 13, values of vapor pressure measured at different temperatures are required. Bevin of the U.S.D.A. at Virginia gathered such data for alfalfa. ihble 5 shows some of his data. It will be used to illustrate the procedure for determining the heat of adsorp- tion. Figure 7 shows a log-log plot of alfalfa vapor pressure vs free water vapor pressure. The values plotted give reasonably well defined straight lines. Their slopes can be measured to get the ratio between the heat of adsorption of alfalfa and the heat of vaporization of pure water. The data indicate that over a wide range there is same curvature to these lines. Therefore, the resulting slepes are good only for the range of from about 85 to 110°? which was plotted. Figure 8 shows the variation of the ratio with.moisture content. As the moisture content decreases, it takes considerable more heat to vaporize the Foisture C ntent (jab) -34- Roy Pavia of the Free tater 40 Voisture Content (idb) Free Via L 8 I‘ 40 —.—-Ma ~.m...— —- 7 96°F i771 1.42 1150? 1120? U;09 2.75- 03 03 (ON) Q \3 I0 I‘D (‘3 H 0 (11 b. l. U '7 .L/ l *TC‘T“ 'v' V Vapor Press 1.05 .59 0 Va 940? 9 1080? v' ’b”—"--".—J— ..— 2.45 2.03 1.8 (“I“) 1. (3? ‘4 H 4: Q0 H I O (D F1 C) ‘2 H 900 1. 2 1 M PB v T"w‘ :4 '._J1 It A at Flacksburg, Virginia) 1040? 1000? 980? .?8 .72 R O 4 O (D o C) C») (i, b (.4 U1 {:32 Li 9.5?59 msnafo: 3.93 acuucou 9.5362 9 -35. .l. 1| 7". . .v . u I. k. v. — .'-‘ 1":- Lf..)> :35 -3394 we vqu .96 £053§> I .m 23ml - C 0‘ m n ...' t ‘3‘. m4 4310M 30 ucnvzpodbA 33 10:4,, 0’; D“D“V Jo UO_I1d..2::Sf any A La 1" 4 J“ v #3 4cm ‘ J _.;..<_ 3 m wki -, ,. a we. poi Loaw> 6:324 ”m1; L363 .3 wgsmmmgm 3.3; ..._ u; a 9m 0v om fiallu,<1xd,fi‘vl.4-543.—uid§ud..4fq _ .. 2.— . ...~ . a t. _ .3-“ I \11 . . { . u ‘4' , .II +. . o... 0.. I n l _ . .1 w 0‘ I .1 ~ .. __l _. ON 0 l . fill . . __ II o m A u . cm W ‘ r M ow U N. w . . a W. _ “0.25 #:waéd Enufloz . - p . . . .111-» L--..1Ltuz!l--; .- ,- Liz”--. . ... . : . Ofi Kw om mm 1.5. on; EL wssuo..ma5vk Sqnmo... l N. 3:?“— ACdLA SAWSSBJJ §O DMWN (5H,.) water in the alfalfa. The data on hard red winter wheat previously given is not complete enough to make such calculations. It was determined at one value of temperature only. The small differences in the equilibrium moisture content curve with temperature are needed to determine the heat of adsorption. If there was no difference, the heat ratio would be unity. Constant tat Bulb Process Consider air rising up through a bin of drying grain. Heat is required for the moisture in the grain to evaporate into the air. If the heat supplied by respiration of the grain is small, and conduction and radiation losses are also small, most of the heat required for vaporization will come from the air. Therefore, as the air rises its temperature will decrease. On the other hand, the amount of water in the air will increase. The sensible heat of the air lowers as it rises through the grain, but the latent heat keeps increasing. The total heat of the air remains constant. As previously stated, the wet bulb temperature lines on the psychrometrio chart are lines of constant total heat. There- fore, under ideal conditions, drying may be considered a constant wet bulb process. Hukill does this in his investiga- 5 tions. It helps greatly in visualizing what happens to the air during drying Operations. ”CS-7* Efficiency of frying 'I‘he overall efficiency of drying may be computed in s masher of different ways. In fast cash writer seems to have his own method. Fundamentally, efficiency equals useful output over input. The useful output for drying is the pounds of water evaporated. The input equals the cost of Operating fans, supplying external heat, special equipment, etc. Labor may even be considered. It is easy to under- stand why there are many ways of computing efficiency. Since smc drying will occur without man's influence, efficiency calculated on this basis may even be over 100 percent in some instances. The thermal efficiency is a better measure of the actual drying efficiency. It is the ratio of host usefully employed in evaporation to the heat supplied. If radiation losses are neglected, the host usefully employed is measured by tho difference between the entering and leaving temperatures (t1 «- te), while the heat supplied can be measured by the difference between entering sir’tcsmersturs and dew point temperature (t1 - to). t - t Theoretical thermal efficiency 3 H 1 10° (14) It is not possible to obtain 100 percent theoretical thermal efficiency even though the exit air be saturated and there are no radiation losses. The smallest value that t2 - 58 - can have is the wet bulb temperature of the leaving air which is always greater than to. .59- 3*"110? F0? on: ERYIEG 1133 Formula 2 gives the drying rate as T = K (p - p‘) (2) v (change in moisture content per hour) ay be written an dfi/at where n in tho moisture content (fldb) and t is timc in hours. gig : x (p - pl!) (15) This expression could be integrated dircctly for n if an analytical expression for (P * P‘} in.tcrms of t were avail- able. Such.an expression is not known, however, and othor means of detonmining the drying tins must be resorted to. The reciprocal of equation 15 in at - , (16) 33' ‘K‘F5‘=13:T A typical variation.of p with‘k has been shown in figure 6. Eith.such.inrormation and K. a curve or dt/Hm vs M can bc computed. in an.oxnmplo, assume I as 10.0fi/(hr)(”flg). Then tho dt/BH curve for the dashed line of figure 6 is as shown in figurc 9. The intogral or this curve vith.roapoct to g is equal to time. Exact integration again cannot be accomplished but may be approximated by summing areas unfier the curve. Area :Jdt I do!" - t (17) Starting at the maximum vaiuo of H tho area or time inoroaccc as M decreases. Practically any degree or accuracy ccn.bc obtaincd if small enough.aron increment. are unod. Tho _oh c;_w.ii _iu,.x.h 1.x». nnn1_m .n not: .\_Jingflnw«H I..; mn:m_* H? mm mu m“ n on um em on O x.) U3 5; H- fl. 1' ) ,c l ,1 if? 3N .r. .\ . resulting time vs h curve is given in figure 10. 11th such a curve it is possible to obtain the time required to dry from one moisture content to another for the given drying conditions. This whole procedure of determining the drying time can be carried out quite simply in tabular form. ihble 4 shows the values used in the illustrative examples of figures 6, 9, 10. The first five columns are self explanatory. In order to get the sixth column accurately a curve of column 5 vs column 1 as in figure 9 is necessary. The area under this curve between the various values of E can be approximated quite accurately. The time value in column 6 for a given value or M equals the area under the curve between the given value of M and h equals 40%. If it was found that (other things being constant) K varied somewhat with H, this var- iation could also be accounted for in column 5. The above discussion assumes a layer of material under uniform drying conditions. That is, p and pa are the same for all parts or the layer. Under actual conditions p and p‘ are not the same for all parts of the layer. Pa will vary as the air pregresses through a drying material. As the air picks up moisture its vapor pressure, p., increases. There- fore, the above calculations are good only for the layer of material next to the point where the drying air enters. Additional calculations are necessary for obtaining the drying rate of that material which makes up the successive layers of the material. TAB-LE 4. - IISTHOD OF ”O‘KPUTIIIG DRETHG TITIE FOR ‘MIEAT Assume: K : 10% (hr)("Hg) u-~-- CD ® CED C5) © 1 l M p p’pa p-pa YUP -pa) t (76b) (from (pa = .41"qg) (or dt/dx) (Area under fig. 5) dt/dU curve) 40 0.74 0.53 5.03 0.305 0.00 54 .74 .33 3.05 .305 1.82 50 .74 .53 3.03 .503 3.03 25 .72 .31 3.23 .323 4.59 20 .59 .28 5.57 .557 6.29 15 .64 .25 4.55 .455 8.24 12 .59 .18 5.55 .555 9.68 9 .47 .06 16.67 1.567 12.68 8 .41 .00 00 00 00 TABLE 5. - COMPUTATIONS FOR LEAVING VAPOR PRESSURE ~— .— nu ——..--. 1..“- ,-a— --.—_—_._-....--,..-.—.... -h.-- - ---. ~.. w—. h-..- .-—.> ® ® ' ® @ © © C7) t p of pa p - pa grains H2O increase Pa first layer entering pound air in p leaving n.a (an) (hours) ("Eg) ("Hg) 70(p - pa) '155 (D..() 0.00 0.74 0.41 0.55 25.1 0.15 0.56 1.22 .74 .41 .5 25. .15 .5 5.05 .74 .41 .55 25.1 .15 .56 4.59 .72 .41 .51 21.7 .14 .55 6.29 .69 .41 .28 19.6 .15 .54 8.2 .64 .41 .2 16.1 .11 .52 9.68 .59 .41 .18 2.6 .08 .49 12.68 .47 .41 .06 4.2 .05 .44 oo .41 .41 .00 0.0 .00 .41 ~43- Considcr air being forced up through a bin of grain. The drying time for the bottom layer is as Just described. In order to get the drying time of the grain at various distances above this bottom layer it is necessary to consider the grain as divided into layers of arbitrary thickness. The thinner the layers the more accurate will be the calculations for drying time. After the drying rate of the first layer is computed, the increase in p‘ leaving the first layer can'be established. The resulting value of pa leaving the first layer will be the pa for the air entering the second layer. The value of p varies with,h in all succeeding layers Just as it does in the first layer. One might think that because td decreases as the air rises, the value of p would also decrease. Because drying is a constant vet bulb process, however, and the value of p is determined from the equation involving t' (equation 12), it can be shown that p varies only with M for any given drying condition. Therefore, the values of p and pa are known for the second layer. Calculation of the drying time for the second (and successive) layer is not the same as for the initial layer. p is given vs M while pa is now given vs time. The procedure is not difficult but is rather tedious. To illustrate, the following example is given: Consider the prdblem.previously worked for hard red winter wheat. Assume a bottom layer with 10 pounds of wheat (dry weight) all of which undergoes drying according to figure 10. Also assume an air flow through this wheat of - 44 - 100 lb dry air/hr. It is first necessary to establish the value of pa leaving th is la; or. Since the drying rats is known, the grain of eater picked up per pound of air can be calculated. K(p - pa) lb H20 7300 grains 10 lb dm, hr. - I x 103 lo dm, hr. lb E20 100 lb air - v _ r. veins 7 3.“) pa) 10 air With this expression and the pay hrometrio chart, the value of pa leaving the first layer can be determined. Table 5 gives this in tabular form for various values of t. The above calculations show that if the air flow is increased or the amountu 3 dry matter in M“ “1 layer decreased, the Erains of moisture picked up per pound cf air will be less. This would result in less raising of pa leaving the first layer and won ld make the drying re .-c of the secs nd layer faster. Table 6 presents a canveu1 'ont me 410d of using: the new values of pa to compute the drying rate of the second layer. The calculations are a stop by step procedure which repeats itself. Column A given values of time shich have been computed for the first layer and the first value of H in coluun B is the orig nal moisture content. A study of the table is self explana Lor y. Columns A and B provide the drying curve for the second layer. Calculations for other layers are similar. Figure 11 shows the resulting curves for several "3 equal 10 pound layers. Figure 11 has been rotated 90“ so that i‘ the ti e is the abscis sea scale. This is the c'uuon method or present tion. ¢ 45 mw.mH oo w.ma n.w oo.m H.m Hm. av. or. H.mm mm.m mo.mH H.Nm bwm ¢¢.H OJH ma. mm.. Hr. m.vN ¢N.w mm.m m.vm v.0 mm.H a.H ma. vm. 0b. m.mm mm.o «m.m m.mm m.n 0b.H m.H ma. mm. vb. b.Hn mn.v mm.© b.Hw m.m mm.H m.H ma. mm. vb. m.vn no.n mm.¢ m.vn m.m HN.H m.H ma. on. vb. b.mn mm.a no.0 b.©n n.n mm.H m.H mH.o mm.o «v.0 0.0¢ oodo NmHH o.ow .. u- u- a- a- u- u- n. 00.0 @-@®©@-®@M ®-@ AGES: A®§§ G ® 5 an a p @ @ © © @ @ ® ® @ @ mmw hnm omen @ @ © © .0 @. @ ® @ l\ltrull. I... lu.l.'.l!llblll lit.--‘ 't.l mEmd ho Wm1 ’ - O . , kg .A x v ‘ t D v O O r 1 r.“ -- ‘ p'w‘tv-w ‘ '~-~,, .*‘.-'~ "in! Y7“") -‘ ‘ *r""nn t. r, ’ k ' ‘I * ‘i‘, ' .5. ‘ ‘. L ' - I - ‘ A 5 . - ’ . .4 t §" - ‘. . a . rv . ' ' -~ '_ .A ' "W « L ' 2 , ~ 4‘ .‘xi a 1 I‘m v 4 ‘ ‘ y‘ f ~. T,- ‘ s' , . . . . .' ‘w s. . 1 J . . 4" s - i “ t .‘ u 4 I . ' .‘ . x ' a _ ~ ‘ .' .‘ \ u _ I n | \ 3, Va I“ \ : v" r' ' ( “'7 5.: ‘ ' ‘ L ' Y’ x: ; I“ '3 . - \ . . 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" ‘ I L~ - ‘ -‘ . ' ' _ ' v ’ ‘ “ “ ‘ .i. 1 g ‘4 A k. . g .L' a - ‘ Q ~ ". L: t 2 " ‘. -. ~ '- a ,. ,- ‘1 » . -. ~ ~\ 'l w . .i - ' 5 . ! . \ _, s- » o J. .L . -_' __ . . . A‘ v Q ~. \ . '4 ,- f‘ ' ~. ‘-—~ . .~ ‘ - o ,v .- 1 . .. I _ , . : (,7 F“, ; 7 _ 0 y I, . 0- \' I .L. . ‘_. .1. ‘ . - ‘ 4' . “ . 'n ,v- ‘w r“! . \ ~ . . r. ‘ , . '. 0‘ e T '_‘ .‘ . | ‘1 {’7 - r-‘ ' v . v ' I ' ‘ _ g -L I . . . h - . L, .. . g . o . ‘ " "J ", ’3 Q: r 4- -~ ~ , - w. s ,‘ *7 r7 - ~ 0 A- v n, .. g .. ~ . . ‘1 ~- ._ a <. -’ 0‘ 7' ~u ‘ V- 1 r’ L: ‘ ' f f A I o 1 .o- o - ., . . . I. f V_ . . . l a 4 - a h. ‘1 o f .' ' .1. t. (-l J ' . ' .a ‘, Q A _ ~ n S v f. .‘ ' o .1. - o .0 -‘ I. ,- - P‘V - x J. g .A. ' O - (W ‘ " W V‘ ' . ‘ , , ., J. . l . A ' C — vapor pressure during drying can be computed. The method is the some as illustrated in table 2 for sheet. Figure 27 shows the vapor pressure of alfalfa at various temperatures and moisture contents (from table 5), and the dashed lines represent the computed values of alfalfa vapor pressure during the tests. The value or C? for alfalfa was determined from a core. rul study of the test date. The value finally established was 0' s 1.45. I" was computed using this value in the last column or table 7. The complete computations for drying time for all six tests are given in table 9. The last column, time in hours, was calculated in the some manner as the illustration for shoot in table 4. The resulting computed drying curves are given in figures 28, 29, and 50. The test point: shown.on the figures are the values fron.the data of table 8. £33 acmvgu 3320: om om on ow om on Om a w . . M . ........... -5--+‘.-al-l-11-z t; ariiili. ,-lII..-!--.!-,L1!t£39-. airflllrlewril- .mymo‘r mcmmuo mf;u£ m . Utah/x mo mnzmmmnn. 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H 0.00 00000 000 - 00:0 000:0 “0000 H 0 0 a 00.0 .0 0:0 00:0.H u 00 0 .0. 0000 00 oo 000.H 0.0H 00.00 00. 0H0.H 0.0H 0H.00 00.0 000.H 0.0H 00.0H 00.H 000.H 0.0H 30.0H 00.H 000.H 0.00 0H.0H 000 000.H 0.00 00.0 000. 00H.H 0.00 00.0 000. 00H.H 0.00 H0. 000. 00H.H 0.00 00.0 000.0 00H.H 0.00 “mess Aam I QFZA Apr; AQ§-V H 0:1 I a z 0H.0 =0 0:0 00:0.H u 00 0 :300090 .3er0 oo oo 000.H 0.0H 00.00 00.0 0H0.H 0. 0H co co 000.H 0.0H 0.H0 00.0 000.H 0.0H H0.0H 00.0 0H0.H 0.0H 00.0H 00.H 000.H 0.0H 00.0H 0H.0 000.H 0.0 00.0H 000. 000.H 0.00 0H.HH 000. 000.H 0.0H 00.0H 000. 000.H 0.00 0H.0 000 000.H 0.00 H0.0 00. 00H.H 0. 0 00.0 000. 000.H 0.00 00.0 000. 00H.H 0.00 00.0 000. 00H.H .00 0.0 H00. 00H.H 0.00 00.0 000. 00H.H 0.0 00.H 000. 00H.H 0.00 H0. 000. 00H.H 0.00 00.0 000.0 00H.H H.00 00.0 000.0 00H.H .00 0 0 n AmcHSv than I 062w.” Amm:v ADWV Amhflv % Q I Q70.» ABS; ADGVLV H H . .2»; s;:--... 0 0 0 o 0 00.0H =0 000 00:0.H u 00 00.00 n =0 000 00:0.H u 00 0 .02 0000 0 .o 0000 00 oo 000.H 0.0H oo oo 000.H 0.0H 00.00 00.0 0H0.H 0.0H 0H.00 0H.0H 0H0.H 0.0H 00.00 00.0 000.H 0.0H 00.00 00.0 000.H 0.0H 00.00 00.0 000.H 0.0H 00.H0 00 000.H 0.0H 00.0H 00.H 000.H 0.00 00.0H 00.H 000.H 0.00 H0.0H 00.H 000.H 0.00 0H.0H 0H.H 000.H .00 00.0 000. 00H.H 0.00 00.0 000. 00H.H 0. 00 H0.H 000. 00H.H 0.00 00. 000. 00H.H 0.00 00.0 000.0 00H.H 0.00 00. 0 000. 0 00H. H 0.00 - . .m n. . 0.000 000 - 0000 000.0 00000 0.000 A 0 - 00 000.0 000,0 H H -smgi. 0 z {:w.:i 0 2 H0.0H =0 000 00:0.H u 00 00.0 n =0 000 00:0.H u 00 n .02 p005 H .02 #000 000000 000 000000000000 . .0 00000 Content (7033:) Moisture m U" N O -73- ”-.-ngifiww_ .“ _‘ fl _ “’0‘. _“,_ '_ _ .0. Figure-2 3.5} .- Comparison of Com- putea Cu/ with Test Data. ’“ Computed O TEbt No.‘ X Test No.2 5 i0 i5 20 25 30 Time (hairs) Content (37065) Moisture .73“ - _. -1“ _ ._. i .H i i K i i I i .. 1 i i i I D i Figure 23. Comparisen of Com- puted perv—es. with Test Data. Lu , ...) } N U1 i N O IS ‘0 * —-——-— @de 0 Test i“-~io.3 , . g x Test N04 _ g, . U1 ‘ __" A __J' is 2.0 25 30 E Ti me (hCUFS) C) (1) E3 35 (c/od‘c) Content m n) 0 U1 Moisture Cn— ES -74. ..+.._.,__~_-_,_,____,..___.._.....-,.._-.._.. ”—..”...0 - m".-- 0 .. me. ,_ ._-._-0-_..._.__, -. 0.-....04.- _..... Figure 550 .“‘ Comparison of Ccm- puted Curves with Test Data. ..__.__ Computed 0 Test No.5 _. .---__ X Te st No.6 ”M. t i 1 i0 is 20 ‘ 25 30 Time (incurs) DISCUSSIGH 0P 'i'IIE RESULTS Agreement of Data and Theory The data in figures 28, 29, and 30 are for test: mode under widely varying conditions. She air flow varied from 8.85 to 16.20 lb or air/(hrHlb dry matter). The original moisture contents for the teat: varied from 29.85'to 48.1%. Two air temperatures were used, 100°? and 120°?. The toot data agree fairly well with the computed curves in all cases. Figure 28 shown the results for two tests which.woro alike in every respect except original moisture content and air flow. That no. 8 has an air flow per pound of dry matter over twice on great no for test no. 1; Test. 3 and 4, given in figure 29, are for other values of original :moiaturc content and air flow. Toot: 5 and 6, given.an figure 30, represent two tests that were practically alike in every respect except temperature of the drying air and original moisture content. The agreement of theory and data is quite good even.with all these variations in tent conditions. One very noticodblo characteristic of the computed curve: in that thwy all tend to 110 above the test data at first and thon.bclow the test data when the drying approaches the equilibrium.value (represented by tho horizontal dashed line). Ehore may be several reason! for this tendency. The - 75 - equation.ueed to compute the curve: (equation 18) ie only approximate and this fact may account for some or the discrepancy. Another possibility in that K" may vary slightly during the drying procure. It baa been pointed out that the "velocity effect" may cause some variation in drying /rate. The velocity tende to influence the drying rate at high moisture contents while at low moisture contents its .ffcct is negligible. This would cause the actual drying rate to decrease factor than the computed value which assumes the velocity effect constant. Thin is the trend in the data. Before the theory can be properly Judged it will be necessary to have considerable more test data. The small amount or data included herein only serves to show that the theory does have possibilities. Drying tceto uith.other values or absolute humidity and other crOpo are necessary. Alec, the tests should give the moisture content: at various levels instead of the overall values. Regardless of thin lack of outctantiation, the theory in develOped in a sound logical manner and can he need to show the relative importance or various factors to drying. the data does outstantiate the theory curriciently to enable one to use it to predict the effect or temperature, humidity, air flow, etc. on drying. Influence of Temperature If the temperature of a commodity is increased, its dry- .7?- ing rate increases. Figure 6 than that the vapor'preeeure or e eubetence increases rapidly when its temperature increases and ac p increases the drying rate e increases according; to equation 3. Electing of the commodity in the result in convection drying when the air is heated. Actually the heated air itself has no real advantage (provided it had sufficient moisture carrying capacity). It in the consequent heating of the product which. produce. the desired increase in drying rate. It would be much more efficient to heat the material to be dried directly rather than to heat the air. ‘On the paychrometric chart it can be seen that the process or heat- ing air only results in moving horizontally to the right across the chart. True, the relative Immidity is lowered, but the vapor pressure which. influences the drying is not changed. Influence of Hmidity It in the absolute hmidity and not the relative humidity that in the important factor in drying. A: the absolute humidity decreases the vapor pressure p“ decreases and this means an increased drying rate. A low relative humidity. however, does not necessarily indicate a low vapor pressure. The psychrOmetrio chart above, that air with a low relative humidity can have a high vapor pressure if the temperature of the air in increased. moratore, when talking -73- about low relative humidity being good for drying it is also necessary to specify the temperature. liffoo t 01‘ Depth The depth.of grain or hay is an important factor in drying. Consider air rising up through.a bin of grain. than drying first starts, the moisture content of the product being dried is uniform and if it is high enough, the tempera- ture of the grain throughout the‘bin assumes the wet bulb temperature or the drying air. The vapor pressure of the grain, therefore, is constant throughout. The vapor pressure of the air, however, varies as it rises through the grain. is the air picks up moisture in the lower areas, its vapor pressure is increased and gradually gets greater as the air rises. The difference in vapor pressure and therefore the drying rate decreases as the air rises through the grain. This fact causes uneven drying. Influence of Air Flow Increased air flow will result inunore even drying and a faster overall drying rate. The data show this quite clearly. As mentioned above, the vapor pressure of the air increases as it rises through a bin of grain. More air means less moisture to carry per pound or air and this means less rise in vapor pressure. This accounts for the increased drying rates of the upper layers with.high air flow. A disadvantage of high air flow is that the efficiency of drying will be low. The air'sill not have enough time to pick up its maximum quantity of moisture. Effect of Ecnsity Varying density does not effect the drying rate as long as the pounds of dry matter remains constant. For example, varying the volume occupied by ten.tons of hay will not change the drying rate or ten tons if the air flow remains constant. The bottom, middle, and top layers, etc. sill still dry in the same manner. This is so regardless of Whether the ten tons of hay is in a tall narrow mos or a wide low new.3 however, if a given volume of hay is considered and the pounds of hay in this volume vary while the air flow remains constant, the more pounds the lower the drying rats in the upper layers. This is understandable because the cir‘sill pick up more moisture as it rises and p3 vill.be higher in the upper layers. One important factor against high densities is that the greater the density, the more static pressure required to force a given.anount or air through it. This results in high priced fans and large poeer”bills. Also, uneven drying may result because the air will tend to go through any channels of lower resistance that may occur and not pene- trate the dense areas. “(30.- Type of materiel The drying characteristics are different for each neter~ iel being dried. In fact they vary within.e material when it 13 prepared in a different manner. Crushed hay for example dries differently tram regular bay. The reason is probably the more exposed water surface area and lean distance for the mpisture to diffuse through to reach the surface. The factor K in.the drying rate expreseian in to take care of these differences between.materiela. Also the vapor pressure 1- mniaturo content curve varies somewhat with 'different meteridll. This makes p in.the drying rate expression different for various enteritis and helps to account for the many shape: or the drying curve. moisture Content then a material being dried bee free moisture, it: vapor pressure and drying rate remain.eonetnnt an the moisture ecntent decreases. After the free moisture has been.evapar- nted, however, the vapor pressure of a material varies with its moisture content. If everything else is held constant leaatnoieture mean: lean vapor pressure. since the drying rate 13 preportionel to the difference between the cummodity and the surrounding vapor pressures, the drying rate decrenaee an the moisture content deoreanon. #81.- CflCLUSIQE 1. A material will dry when the vapor pressure of the water in the material is greater than.the vapor pressure or the water in the air ourrounding the material. 2. The rate of drying is preportionel to the difference between the vepor pressure or the material and the vapor preesure of the surrounding air. This relationship may'bo expressed as Drying finto = K (p 0 P.) where K is a proportionality factor, p in the vapor preeeure of the material. and p‘ is the vapor pressure of the enter in the air. The experimental results conducted on alfalfa hey indicate that this relationship is approximately true. Considerable more data in neeeeeary to estatliuh it definitely. 3. If the preportionelity factor it known for a given material the expression for the drying rate, givendbove, een.be solved for the time required to dry from one moisture content to another. 4. than the temperature of a material it increased, its vapor pressure increases, and the result is a fatter drying rate. 5. than the absolute htmidity of the air in lowered, the vapor pressure or the water in the air decreases, resulting in foster drying . 6. The vapor pressure or the air is increased as it passes through a drying material at a rate which decreases as the air flow increases. The result is faster overall drying when the air flow is increased. ’7. As the moisture content of a drying materiel pregrescively decreases, its vapor pressure decreases, result- ing in slower drying rates. than the vapor pressure or a drying material has decreased to that of the surrounding air, the drying rate is zero and the material is at the equili- briun moisture content. 8. The density of a material does not influence the drying rate so, long as the pounds of sir/(hopround of dry matter) remains constant. It the pounds or dry uttor in a given volume in increased, however, while the air flow is held constant (such as so many era/rt!a or m ares), the drying rats rill decrease. 1- 4- 5a 5- 7- 8c- 9- 10- 11* 1.13175 "3‘33? CI‘I'JD Barre, R. J. 1933 Vapor Pressures in StuAyinr Z‘olsture Tranafsr Problems. Agricultxral ?"“nAer’:g, 10: 247-249. 378314031, F. C. 1341 Storage of Grain Sorghuma. [rrlculm rel Enggneer~ 333. 3g: 185-1333. Kahlil, Silliam V. 1947 Basic Pr‘l nciplea in Drying Corn and Grain Sorghums. LA Azricultural Engineerirgg. g3: 335-353, :40. [19318 Ff. 31'. 193 The Rate or prying of.5011Satariala. The Journq; of Industrial ané :nr'. nearing GizarUiatr*, 427-432. $210m00d. To K. 1932 ‘Iie Dryizig of'°A011da. The Jburnal or Industrial and Engineering hamiatry, §£;753?-312. NGWTTAfln. A. B. 1931 The Dryln; of Porous Solids: Diffusion and Surface Emission Squatiovs. firnnsnotiona of tha A erican Inaticute of Chemical'Shginaara, =_5 avd- . Carrier,‘S. K. 1913 Temg. erasure of Evaporation. Transactions of the American Sooiet of Eaati 33 uni ventilating // Efifijnears. gig'fiszza; ' Carrier, S. H. 19% 3A9 "hsory of AtAospheric Svap oration w1th Special Reference to CoApartAsnt Dryers. Journal of Indxxetrlal and A glaaaring Cnamlstny, 13:35A-458. Karks Lionel S. 194i F00228n1 cal Sng?raaer’s Ifandbook, fourth Adltion. AaG.aw-Sill fooA CompAny, Incorporated, Saw York: 1632-1699. Parry. John H. 1941 Ineer'a Handbook, Second Ldition. A00; Catapuny, Incoryoratod, Saw York: Chemical S 1440‘]. floatin. Ventilatin» Air Cond'ticnlnr Guido. - ~ -: .er can Society of Seating and Ventilating LngAneorB, Kflw Vorkx "09.725. 13¢ 14- 16- 17- 19- -84- Joy, F. A. and Queer, E. R. 1943 Permeance Measurement Improved by Spocial Coll. Heating Piping and Air Conditioning, El, June: IDS;110. Goff, John A., ot.al. 1949 Standardization of Thermodynamio Properties of Foist Air. Heating Pipi.n: ind Air Conditioning 21, Hovember: 118-126. Keenan, Joseph H. and Reyes, Frederick G. Thornodynanic Properties of Stoao, First Edition. John'%lloy and Sons, Incorporated, Few York. 1936 Arnold J. H. The Theory of too Psychrometer. Pb sics, 4: 1935 255-2 82. International Critical Tables, First Edition. Fe Sraw-Hili'oook Ebmpany, Incorporated, New Yor: 1928 Volume I, Farvin, C. F. 1941 Psyohrometrio Tables for Obtaining the Vapor Pressure, fielativa Humidity, and Femperaturo of the few Point. united States Department of COQfifiPCQ. fin Bo fiOQ 255- carriar’ f". H. 1911 national Psychromotrio Formulae. Transactions p09 71. of the American Society o.{_Fo chanical finginaora, 3 Qt)" cull-ID JHU g Legault, R. 8., Fakowor, Bonjan in, a:1d Talburt, F. F. 1948 Wilson, lfigl Dexter, 1947 1925 Apparatus for Feeauromont of Vapor Pressure. Analytical Cheniatrg,‘§22 428-430. R. E. Humidity Control by Foams of Sulfuric Acid Solutions. Chemistry, Journal of Industrial nod Engineering $.23 3L" U-Sullc so To. Shsldon' at £0, and fialdron, DOPOthy I. Equilibrium Eoioturo Content of Alfalfa Hay. Agricultural Engineering, 28: 295-296. ' Fellows, H. C. and Coleman. D. A. ./ fiygroscOpic Foisture of Cereal Grain and Flax Seed Exposed to Atmosphere of Different Relative Humidity. Cereal Chemistry, g; 275-287. 2‘4- Otmer. 1940 0 ”fit Tho Thermodynamics of Key Briers. Ehccia for t” Ph. E., Cornell Enivcrai y, Ithaca, Few York. Dana 16 F0 Correlating Vapor Pressure and Latent Boat Data.o' Journal of Inductrial and Engineering Chcmiatrz, 32: 841~855. . m {zoom USE ONLY . ‘7~ '0 M'TlTliWQITILfijifllLNfi!flifliflfliflflyfljfijfimfiES