4. How a psychrometer works
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1 1 4. How a sychroeter works Identical theroeters Dry bulb (war Gauze around the wet bulb ool water Wet bulb (cool Saturated air Huidity to be easured T dry at Water being condensated, waring the gauze Water being evaorated, cooling the gauze T wet at OUT (cool IN (war vaor Water being evaorated, cooling the air vaor DRY-AIR ixture air-vaor vaor DRY-AIR Fan ulling the air fro the device Volue V IN Volue V OUT HOW A PSYHROETER WORKS On each second, a ass of water evaorates, cooling a ass DRY-AIR of air Figure 1: How a sychroeter works Figure 5 shows in details how a sychroeter works. Each second, a net ass of water vaor is evaorated, cooling a ass of air air. In atheatical ters, according to the first rincile of therodynaics (conservation of energy: Heat to vaorize the water Heat fro the cooling air T DRY AIR P (1 where: T T DRY - T ("Wet Bulb Deression" ean latent heat of vaorization of water fro o to 50º 584 cal / gra of water ass of liquid water being vaorized to be deterined DRY-AIR ass of air being cooled to be deterined DRY-AIR-P sensible heat caacity of air at ct. ressure cal / gra / º
2 2 T absolute teerature of ixture air-vaor (dry bulb teerature t º T absolute teerature of wet bulb t º All that follows is a consequence of this sile equation (1. changes with teerature (see Fig. 6, but since in the range 0-50º the change is relatively sall, to silify the calculations the average value is used. In the sae range, DRY-AIR-P is ractically constant. Figure 2: Latent Heat of Vaorization of Water Equation (1 ay also be written as: AIR P T (2 AIR In the volue V IN (Fig. 5, there is a ixture of DRY-AIR gras of dry air and gras of water vaor. According to the Ideal Gas Law (Annex A: V R T IN DRY R T V DRY IN (3 Using the Dalton Law (Annex B in volue V IN DRY-AIR + and defining the Huidity Ratio HR (or Absolute Huidity: HR / DRY-AIR (4
3 3 equation (3 becoes where HR (5 olecular ass of water vaor 18 gras/ol DRY-AIR olecular ass of dry air (weighted average 29 gras/ol local atosheric ressure (Hg artial ressure of vaor at T DRY (to be deterined The olecular ass of dry air is calculated as follows: olecule % Vol ol Product Nitrogen (N Oxygen (O Argon (A arbon Dioxide (O Su ol of Dry Air Using the sae reasoning in volue V OUT (Fig. 5, a siilar relationshi is found: + HR + (6 DRY AIR where is the saturation ressure of water vaor at T (Annex. Subtracting Eq. (6 fro Eq. (5 and equating it to Eq. (2 results: DRY AIR P T VAP (7 Defining the "Huidity onstant" k as: k 0.24(cal / gra /º 29(gras / ol 584 (cal / gra 18(gras / ol DRY AIR P Note: cal / gra / º cal / ( gra º equation (7 becoes: º k T (8 In Eq. (8 the only unknown is which is equal to:
4 4 ( 1 k T k T ( 1 k T k T (8 where (Annex : (tº ( * e S * t t + Hg Eq. (8 ay be silified, considering the nuerical values of soe of the ters: (9 1. T ºK t º by the definition of the Kelvin scale. 2. If Then 0 < T < 20º and k / º k T < << 1 So, 1 - k T ~ If t < 50º and (50º 100 Hg and ( Hg < < 760 Hg Then k T (t < 1.3 Hg << 127 Hg < So, k T (t ~ 0. Silifying eq. (8, the Psychroetric Equation becoes: (t k t (10 a well known relationshi. Finally, the Relative Huidity (RH (see Annex ay be calculated as: RH % 100 (11 (t DRY OBS: It ay be noted that the so called "Psychroetric onstant"
5 5 Exale: AIR P γ ε VAP was not used here because it is not a constant (deends on ; (k was used instead. When the local atosheric ressure is 760 Hg (sea level, the teerature of the dry bulb is 20º and the wet bulb is at 15º, the relative huidity is 58.6%: * S (20º ( * 7.5 e Hg S (15º Hg k T (1/º * 5º * 760 Hg 2.52 Hg Hg RH% 100 * (10.22 Hg / (17.44 Hg 58.6 % Note: 1 kpascal Hg Precision of the easureent when using exression (10: To reduce the easureent error, three recautions ust be taken: 1. The sychroeter ust be insulated fro the radiant heat of the environent (infrared rays. This ay be accolished by surrounding the wet bulb with a reflective surface (e.g. aluinu foil, but leaving a sace for ventilation between the foil and the gauze. 2. Although ideally distilled water should be used to oisten the gauze, in ractice, using filtered drinking water ay be sufficient. 3. The wet bulb ust be ventilated, to avoid the foration of a saturated-vaor layer around the wet bulb, which reduces the evaoration, thus increasing its teerature. Ventilation ay be set around one eter er second. As a reference, a sall fan (38 x 38 x 10 for a 486-PU, oerates at an air-seed of 1.6 eters er second (this fan costs around US$ 12. Here is a real exale using lab data on given date X: Site altitude: 637 eters (fro htt:// Dew oint teerature (easured: 8º Dry bulb teerature: 18.5º (abient teerature Wet bulb teerature: 15.0º (Augustus Psychroeter, no ventilation Wet bulb teerature: 12.5º (Augustus Psychroeter, ventilated 1 eter/second oercial electronic huidity eter (caacitive: 51% alculated relative huidity (using "Quick_Start.xls": Using sychroeter, no ventilation: 69.9% (error Using sychroeter, with ventilation: 50.5% (no error Using Dew Point and abient teeratures: 50.5% (reference
6 6 Here is another real exale using lab data on given date Y: Site altitude: 637 eters (fro htt:// Dew Point teerature (easured: 9.9º Dry bulb teerature: 25.3º (abient teerature Wet bulb teerature: 17.5º (Augustus Psychroeter, no ventilation Wet bulb teerature: 16.0º (Augustus Psychroeter, ventilated 1 eter/second oercial electronic huidity eter (caacitive: 36% alculated relative huidity (using "Quick_Start.xls": Using sychroeter, no ventilation: 47.0% (error Using sychroeter, with ventilation: 38.4% (sall error Using Dew Point and abient teeratures: 38.0% (reference NOTE: All the equations and the calculations used in this article were develoed and tested with atheatica 5.0 (Wolfra Research, a highly recoended software.
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