humidity

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Chapter 10: Air - Water Vapor Mixturesb) The Psychrometric Chart and Air-Conditioning ProcessesWe notice from the developrnent in Section a) that the equations relating relative arrd specifrchumidity, temperature (wei and dry bulb), pressure (air, vapor) and enthalpy are quite tediousand inconvenient. For ftis reason a Psychrometric Chart relating all the relevant variableswas developed which is extemely usefirl for designing and evaluating air-conditioning andcooling tower systems.

At first appearence the psycbrometric chart is quite confirsing, however with some practice itbecomes ar exfemely useful tool for rapidly evaluating air-conditioning processes. The mostpopular chart in common usage is that developed by ASHRAE (Americaa Society ofHeating, Refrigeration and Air-Conditioning Engineers), however we feel that theconstruction ofa simplified version ofthe chart based on approximations ofthe variousequations can be a very usefi:l tool for developing an understanding of ifs usage. Thisapproach was suggested by Maged El-Shaarawi in his article "On the Psycbrometric Chart"published in the ASHRAE Transactions @aper #3736, Vol 100, Paxt 1, 1994) and inspired usto produce the following simplified psychrometric chart:

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11f25t?o14 clEFter 1ft| Ihe Ptychcret c c@(u@47t212o14)The basic information used to construct the chart is the water vapor saturation data (Tsat, Pg)which is obtained from sieam tables over the range from Tsat = 0.0 I 'C tbrough 50"C. Thespecifrc humidity rrr is then evaluated using the relative humidity q as a parameter to producethe various relative humidity curves (blue lines) as follows:

where P is the standard atrnospheric pressure 101.325 [kPa].The saturation curve (100% relative humidity) also known as the dew point cuwe is drawn asa red line. Notice that on the saturation curve the wet and drv bulb temperatures have thesame values.

The major simplifuing assumption in the construction of the chart is ihat the enthalpy ofthemixture is assumed to be constant throughout the adiabatic saturation process (described inSection a). This implies that the evaporating liquid added does not significantly affect theenthalpy ofthe air-vapor mixture, leading to the constant slope wet bulb temperature /enthalpy (red) lines defined by:

nair'+'xtrltrug ctry ai' l= T['c] + tp.ti:-m +lT['c])wftiell is tulthe! Anally rduc:ed te:

r***,[']ft * o.]* r['e + 15ooroslthaipyNote that on the ro = 0 axis (dry air) h = T fcl

Finally, the specific volume oftle air-vapor mixhre (green lines) is determined fiom theideal sas relation as

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where the gas consta:rt R6 = 0.287 ftJ/kg.Kl

It is normal practice to separate out tlre overlapping enthalpy / wet bulb temperature linesallowing them to be separately evaluated. Thus we introduce an oblique enthalpy axis andentha$y (black) lines as follows:

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The four equations higblighted above were programrned in MATLAB and used to plot thesimplified psychrometric charts shown above. Refer to the link:MATLAB program for plotting a Simplified Psychrometric Chart

Ar excellent Nebcuide (Jniversity ofNebraska-Lincoln Extension Publication) on How touse a Simplifred Psychrometric Chart has been provided by David Shelton, and is alsoavailable as a pdf-Iile (968k). This guide reduces the confusion by separately explaining 4 ofthe 6 sets of curves which make up a psychrometric chart. Definitely read this guide beforecontinuing.

Solved Problem 10.1 - Assume tlat the outside air ternperature is 32oC with arelative hunidity g : 60%. Use the psychrometric chart to determine tle specific humidity to[ 18 gm-moisture,&g-air], the enthalpy h [78 kJ/kg-air], the wet-bulb temperature T*6[25.5'C], the dew-point temperature T6o [23"C], and the specific volume ofthe dry air v10.89m3,&gl. Indicate all the values determined on the chart.

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Solved Problem 10.2: Assume that the outside air temperature is 8"C. If the air in ardom is at 25oC with a relative humidity E = 40%, use the psycbromehic ehart to determine ifthe windows of that room which are in contact witl tle outside will become foggy.

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The air in contact with the windows will become colder until the dew point is reached. Noticethat under the conditions of25"C and 40% relative humidity the dew point temperature issltghtly higher than 1 0'C, At that point tle water vapor condenses as tle temperatureapproaches 8'C along lhe saturation line, and the windows will become foggy.

One ofthe major applications ofthe Psychrometric Chart is in air conditioning, and we findthat most humans feel comfortable when the temperature is between?Z"C and27'C, and therelative humidity I between 40% and 60%. This defines the "comfod zone" which isportrayed on the Psycbrometric Chart as showa below. Thus with the aid ofthe chart weeither heat or cool, add moisture or dehumidif as required in order to bring the air into thecomfort zone.

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Solved Problem 10.3: outside air at 35'C and 60% relative humidity is to beednditioned by eooling and heating so as to bring the air to witlin the "eomfort zone". Usingthe Psychrometric Chart neat$ plot the required air conditioning process and estimate (a) theamormt ofmoisture removed [ 11.5g-H204rg-dry-air], (b) the heat removed [(l)-(2), q.oot :48kJ&g-dry-airl, and (c) the amount ofheat added (2)-(3), q,"os = 10kJ,&g-dry-airl.

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Solved Problem 1 0.4 : : Uot ary air at 40"C and 10Yo relative humidity passes tbroughan evaporative cooler. Water is added as the air passes through a series ofwicks and lhemixture exits at 27oC. Using the psycbrometric chart deterrnine (a) the outlet relativehumidity t457"1, O) the amormt of water added [5.4g-H20lkg-dry-air], and (c) the lowesttemperature that could be realzed [18.5"C].

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This type ofcooler is extremely popular in hot, dry climates, and is popularly known as aSwamp Cooler. An interesting application ofusing a swamp cooler to cool drinking water inextremely hot environments is described in the posting of Rich Oppel in the At War blog ofthe New York Times: 'Drinking From Socksr

An interesting and informative description on Psychrometric Chart Use for livestock andgreenhouse applications has been presented in a University ofConnecticut website byMichael Darre. Other websites tlat we found interesting is that of g{ikipcdia onPsychromeaics, and one by Sam Hui (Hong Kong University) on using the psychrometricchaxt in the 'Climatic Design of Buildings'.

On to Section c) Cooling Towers for Steam Power PlantsF

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humidity

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