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The Theory of Psychrometry John R Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1953 The theory of psychrometry John R. May Iowa State College Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Chemical Engineering Commons Recommended Citation May, John R., "The theory of psychrometry " (1953). Retrospective Theses and Dissertations. 12728. https://lib.dr.iastate.edu/rtd/12728 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscnpt has been reproduced from the microfilm master. UMI films the text directly from the ongina! or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning tne original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. ProQuest Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 NOTE TO USERS This reproduction is the best copy available. UMI Thii THiOHY OF rSYGHiiOWHrSY by John E. May A Dissertation Submitted to the Graduate Faculty in Partial Pulflllment of The Requirements for the Degree of DOOi'OH Of FhlLOSCPKY Kajor Subject:• Chemical• • • • Engineering Approved: Signature was redacted for privacy. In Chart^e of Major Woric Signature was redacted for privacy. ,-iead of Major Depai^me^ Signature was redacted for privacy. Dean oi Graduate College Iowa State College 1953 UMI Number; DPI2054 UMI UMI Microform DPI2054 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 11 OF COl^T ii-OTS Page AriSI .lACTjj V I. II.'^'hODUC'xIOi^ i II, ICAL CoNi.IiJjiiiALIOi'.S 8 A. inilsslvlty of a Mercury-Glass Ihermometer S 5. Psyciirometrlc Equation 12 1. Fluid ilov^ 14 2. ..eat transfer 46 3. Hass transfer 72 4. Equilibrium during the simul­ taneous exchange of heat and mass between the wall of a cylinder and a fluid in tur­ bulent flow 82 5. A..plication to the wet-dry- bulb psychrometer So III. iiXPr.iiJl'i£m'AL llo IV. TiiiAxnx^i'i OF DAI-A A.ND ik^ULvS 132 A. Emlssivity of a iiercury-Glass Thermometer 132 3. Psyciirometric Tests 14C V. DISCUSSION Itc VI. CONCLUSIONS 158 VII. CIIjiD 16C VIII. ACru'jOw'Lr.DGi'iiiKTS 165 IX. AP?i:-I.JlX 166 r I oil 7 ill LIST OF T^LiiS Page Table 1 Determination of Critical Value of Ee« ... 41 Table 2 Comparison of Values Calculated by iiquations (108a) and Ql3) 62 Table 3 Data and Calculated Values for tne Determination of the iimlssivity of a Mercury-Glass Thermometer lC9a- 139b Table 4 Psychrometric Data and Calculated Values for Water Vapor-Air System 145a- 149b Table b Scnmidt Numbers 151 Table 6 Comparison of VsTf / Values as Given by Equation (194) and 0(Re) 155 IV LIST OP FIGUaiib Page Plgui^ 1 Velocity Distribution in Hound Pipes Near the Wall at High Reynolds Numbers (Predicted) 54 Pigiire 2. Variation of and Jlc X/rQ with y/rQ 57 Figure 3 Tneoretical Velocity Distribution Near tae Wall at Low Reynolds Numbers. 39 Figure 4 Plot for the Determination of "F" 49 Figure 5 Haster Temperature Distribution Plot ... 58 Figure 6 Comparison of Predicted Velocity and Temperature Profiles at High Re 68 Figure 7 Schematic Diagram of Main Apparatus.... 114 Figure 8 Schematic Diagram of Test Section of i4aln Apparatus 116 Figure 9 Micro-Wanometer 121 Figure 10 Plot for Eialssivlty Determination 138 Figure 11 Correlation of Psychrometric Data 146 Figure 12 Correlation of Psychrometric Data 147 Figure 13 Comparison of 0(Be) and HJz I . 156 V analogy between i luid friction, h.eat transfer and mass transler Is used In tnls paper to describe tne behavior of tne wet- and dry-buib psychroraeter. Equations are derived to describe ti^e velocity, temperature and concentration pro­ files lor the flow of liulds through round pipes based on a new correlation of tue Prandtl uilxing lengtr. wit:, pipe di­ ameter for lully turbuxent llov?. 'Jhese equations are extended to apply to ti^e case of How of a fluid at ri^nt angles to a single cylinder. i'he resulting psyciirometrlc equation is ^ Pw ~ Pa ^ b _ (1.C72 + C.S8 — c r "a (?r^/^-l) + C.58 where ^w = vapor pressure of tr^e vaporizing liquid at tne wet- bulb temperature vl ci = partial pressure of the active componer.t actually ^-.resent In the gas stream ? = total pressure ol the system Av = latent heat of va::orlzatlon of the active comi^onent at tne wet-bulb temperature plus the sensible heat required to heat the vapor from the wet-bulb tem­ perature to the temperature at the boundary of the fusion layer t^ and = true gas temperature and wet-bulb tempera­ ture, respectively h^ = modified radiation heat transfer coefilclent: ~ ^wb ^a - ^rb hj, = radiation coelflclent found from modified form of the Stefan-Boltzaann equation: hj. = 0.00692 (~)^] t^ = temperature of enclosure surrounding the thermome­ ters = arithmetic mean of t^ and t^^ expressed in °ii AT = temperature dilference, (t^ - t^^j), in °ii emissivlty of the thermometer taken here as C.9C for the wick vli = convection heat transler coefficient found by: ^ ^^ ^ ^0) ^ * i C# Xog (xie)J c D * ^ d = tneriaal conductivity of gas D = diaffieter of thermometer lie = Reynolds number = T3aP//-^ u = linear velocity of gas flow p = density of gas = viscosity of gas Kjjj = molecular weignt of gas plus vapor it contains K = molecular weight of active component (vapor) c = heat capacity of gas S - Scrimldt number = Dy = diffusivity of vapor through gas ?r = Prandtl number = c/Vk . To determine tne true gas temperature, t^, where the dry- bulb thermometer is subject to radiation error, it is neces­ sary to use a heat balance expressed by Knere t^ = temperature indicated by thermometer and all other symbols are as defined above. vlll The einlsslvi"cy, 6^, to be used in the term in this case would be that ol a plain neivjury-glass tnermometer which Is shown to be C,73. Equations are also given here to predict friction factors lor tiie flow of a gas at right angles to a single cylinder. All of the equations given apply whetner t;ie system used is tne common air-water vapor system or any other combination of gas and vapor, providing the physical properties are known such as c-O to maiie up the Schmidt and Prandtl groups. Con­ versely, if the properties are not known, tais provides one Way of determining them experimentally. 1 I. li^'i'iiODuVx-ICN The wet-bulb hygrometer Is a valuable engineering and meteorological tool, the use of which dates back as far as 1793 when it was used by nutton. Although well over a hundred papers dealt with this instrument over the next one hundred fifty years, no correct theory of its mechanism was proposed until 1952. frlor to 1952,two distinct theories of the psychrometer had been proposed: (a) the convection theory, usually asso­ ciated with the name of August [4], and (b) the diffusion theory proposed by Maxwell [19]. Both theories predict the same (correct) form of the humidity-temperature relationship; however, because of their physical Incompleteness, neither form gives a correct value of the proportionality constant. Empirical correlations by numerous workers over many years have demonstrated that for the system water vapor and air the ratio (P« - - *Kb' A (1) 2 is constant at any given air velocity. The convection theory as advanced by Gay-Lussac [11a], Ivory [14], August [4], and Apjohn [2] predicts tnat the quantity A is equal to whereas the dll'luslon theory ol haxwell led to the quantity Because tne value ol A in equation (1) is not, in gener­ al, lound experimentally to be exactly equal the value of A as given by either the convection or diffusion theories, it has long been the practice to determine A experimentally and employ it in tae form of tables. The form of the iunction needed to correlate values of A is easily determined from such data. Thus Grossmann [12] proposed an empirical equa­ tion in which the A quantity was expressed as A whei^ a and b are empirically determined constants, and u is the air velocity. Weber [31] and Svensson [3Cb] independently proposed the form A 3 where S Is the Schmidt number//jplx^accA Pr Is the Prandtl number of edr, C/z/k. It Is clear that a correct psychrometric theory should predict a value of A that will be valid, not only for air and water vapor, but tor mixtures of any solute vapor and carrier tas, a requirement that the foregoing equations were unable to neet.
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