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Humidity Sensor Moisture and Psychrometrics

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Humidity Sensor Moisture and Psychrometrics Humidity Sensor Moisture and Application Sheet Psychrometrics MOISTURE PSYCHROMETRICS Measurements involve different terms and units. Moisture Deals with the thermodynamic properties of moist gases while terms and units all fall under the area of psychrometrics, the the term “humidity’ simply refers to the presence of water vapor study of water vapor concentration in air as a function of in air or other carrier gas. temperature and pressure. Selecting a moisture terma depends on the application. Psychrometrics concerns mixtures of water vapor and dry air. Much of it also applies to other carrier gases because the Dew points and frost points are often used when the dryness of thermodynamic characteristics of water vapor are fairly the gas is important. (Moisture condensation from gas at low independent of the carrier gas. In addition, as the composition process temperatures must be avoided). Dew point is also of atmospheric air is fairly constant, dry air is treated as used as an indicator of water vapor in high temperature homogeneous gas with a molecular weight of 28.9645. The processes, such as industrial drying. molecular weight of water is 18.01528. Mixing ratios, volume percent, and specific humidity are usually PARTIAL PRESSURE used when water vapor is either an impurity or a defined The gas laws say that the total pressure of a gas mixture is the component of a process gas mixture used in manufacturing. sum of the partial pressures of the constituent gases. Also, the Mixing ratios are also used, like dew point, in industrial drying. volume ratios of constituent gases are equal to the ratios of their partial pressures. For example, atmospheric pressure is ρ Relative humidity is most commonly used in HVAC (Heating, the sum of the partial pressures of dry air and water vapor ( ATM ρ ρ ρ Ventilation and Air Conditioning) applications where it directly = = A + w). impacts human comfort and indoor air quality issues. Relative humidity is also of interest to process control personnel WATER VAPOR PRESSURE because low RH may cause brittleness and static electricity When a mixture of air and water vapor is in equilibrium with problems, while high RH may cause swelling and clumping liquid water or with ice, it is considered to be saturated (RH = regardless of temperature. (See Table 1.) 100%). The water vapor saturation pressure over ice for the temperature range of -100 ºC to 0 ºC [-148 ºF to 32 ºF] is given TABLE 1. MOISTURE TERMS, DEFINITIONS AND UNITS by: Term Definition Unit Absolute Humidity mass, vapor grams/m3 3 C (Vapor volume [grains/ft ] In()ρ = 1 + C + C T + C T2 + C T3 + C T4 +C In()T Concentration) ws T 2 3 4 5 6 7 Mixing Ratio mass, vapor kg/kg, grams/m3 3 where: mass, dry gas [lb/lb, grains/ft ] Relative Humidity mass, actual vapor % C1 = -1.0214165E +04 C5 = 3.5575832E -10 mass saturated vapor C2 = -4.8932428E +00 C6 = -9.0344688E -14 actual vapor pressure C3 = -5.3765794E -03 C7 = 4.1635019E +00 saturation vapor pressure C = 1.9202377E -07 4 partial pressure, vapor vapor pressure water The saturation pressure over liquid water for the temperature Dew Point Temperature of saturation ºC or ºF range of 0 ºC to 200 ºC [32 ºF to 392 ºF] is given by: (condensation) Volume Ratio partial pressure, vapor % by volume C partial pressure, dry gas In()ρ = 8 + C + C T + C T2 + C T3 +C In()T ws T 9 10 11 12 13 Mass Ratio mass, vapor PPM by weight, where: mass, dry gas PPMW 6 PPM by Volume volume, vapor x 10 PPM by volume, C8 = -1.0440397E +04 C11 = 1.2890360E -5 volume, dry gas PPMW C9 = -1.1294650E +01 C12 = -2.4780681E -9 PPM by Weight PPMV x mole weight of water PPM by weight, C10 = -2.7022355E -02 C13 = 6.5459673 mole weight of carrier gas PPMW Hygrometer Instrument for measuring moisture in gas (from Greek “hydros” – wet, moist) See also Table 2. Psychrometer Instrument using wet/dry bulbs to measure moisture in gas (from Greek “hydros” – wet, moist) Sensing and Control Humidity Sensor Moisture and Psychrometrics TABLE 2. SATURATION VAPOR PRESSURES OF WATER FROST POINT Temp. ºC Saturation Temp. ºC Saturation If measurements are made below the freezing point of water, Vapor Vapor that is if the indicated dew point is below the freezing point of Pressure Pressure water, then the equilibrium occurs at the vapor pressure of ice (mm Hg) (mm Hg) (not water) which is less than that of water. That is, the frost -20 0.8 50 92.6 point is a bit higher than the dew point. -10 1.9 60 149.5 0 4.6 70 233.8 If RH and dry bulb temperatures are known, dew point can be 10 9.2 80 355.3 derived by first calculating saturation pressure at the dry bulb temperature and then multiplying by the RH ratio to obtain ρ , 20 17.5 90 525.9 w the partial water vapor pressure. Now apply the following: 30 31.8 100 760.0 40 55.4 For dew points in the range of 0 ºC to 93 ºC [32 ºF to 200 ºF]: = + α + α 2 + ρ 0.1984 SIMPLIFIED FORMULATIONS Td C14 C15 C16 C18 w The preceding equations are very accurate, but may be overly cumbersome for real time calculation. The following equations For dew points below 0 ºC [32 ºF]: are less accurate; however, they are generally suitable for mid- Td = 90.12 + 26.41α + 0.8927α 2 range calculations as used in HVAC applications, for example: VOLUME RATIO For dew points higher than ice point: Also called mixing ratio by volume, or vmr) is the ratio of water 17.502 × T vapor volume to dry air volume (V /V ). Because the volume = []+ × − × × w a e 1.0007 P 3.46E 6 6.1121 exp 240.0 + T ratios of mixed gases are the same as their partial pressures, volume ratio can be expressed as: For dew points at or below ice point: ρ 22.452 × T = w ρ = ρ + ρ = []+ × − × × VR ; w a e 1.0003 P 4.18E 6 6.11215 exp ρ 272.55 + T a where: ρ Because total pressure is the sum of partial pressures, the e = w vapor pressure in mbar (one psi = 68.94745 mbar) partial pressure of dry air can be readily derived (once vapor P = total pressure in mbar (1atm = 1013.25 mbar, 14.696 pressure is known) by measuring total pressure directly or by psia assuming one atmosphere (14.696 psia) total pressure. T = temperature in ºC(ºF = ºC x 1.8 + 32) Multiply the ratio by one million to obtain ppmv (parts per million by volume). RELATIVE HUMIDITY The ratio of the partial vapor pressure to saturation vapor HUMIDITY RATIO pressure at the dry bulb temperature: Also called mixing ratio by weight, or wmr), is the ratio of the mass of water vapor to the mass of dry air. To calculate this, ρ ρ ()T multiply the volume ratio by the ratio of the molecular weights. RH = w = ws d ρ ρ ()T ws ws M 18.01528ρ ρ W ≡ w = w = 0.62198 w ρ ρ ρ Ma 28.9645 a a where WS(Td) is saturation pressure at the dew point ρ temperature and WS(T) is saturation pressure at the dry bulb temperature. Relative humidity is moisture and temperature The humidity ratio, in common use, is expressed in kg/kg, or dependent but independent of total pressure. If dew point and g/kg [lb/lb, grains/lb]. (There are 7000 grains in one pound.) dry bulb temperatures are known, then RH can be derived by Multiply the ratio by one million to obtain ppmw (parts per calculating saturation vapor pressure for dew point and for dry million by weight.) An engineer may, for example, combine a bulb, then applying the RH definition above. humidity ratio value with the reading from a mass flow meter to calculate the mass of water vapor flowing through a dryer DEW POINT exhaust duct per unit time. Is the temperature at which a given sample of moist air is saturated. If the sample is cooled below dew point, then water vapor begins to condense. This phenomenon is the basis for various chilled senor type dew point meters. 2 Honeywell • Sensing and Control Humidity Sensor Moisture and Psychrometrics VOLUME PERCENT STANDARD ATMOSPHERIC DATA Equivalent to 100 times the mole fraction; the ratio of water Normal atmospheric pressure variations have small effects on vapor volume to total volume, Vw/V or Vw/(Vw + Va) expressed calculations that require a value for total pressure. However, at as a percentage. Like the volume ratio, it can be calculated in higher altitudes, atmospheric pressure variations become terms of partial pressures: significant. The following standard data is adapted from NASA. At sea level, standard temperature is 49 ºF and standard ρ barometric pressure is 29.921 in Hg. (See Table 3.) V% = w ;= ρ = ρ ρ w a TABLE 3. STANDARD ATMOSPHERIC PRESSURE DATA SPECIFIC HUMIDITY Altitude (ft) Temp. ºF Pressure Normally expressed as a percentage, is the ratio of the mass in Hg psia of water vapor to the total mass, and may also be calculated in 0 59.0 29.921 14.696 terms of the humidity ratio: 500 57.2 29.38 14.430 1000 55.4 28.86 14.175 M W 2000 51.9 27.82 14.664 q = w = + = + Mw Ma 1 W 3000 48.3 26.82 14.173 4000 44.7 25.82 14.682 ABSOLUTE HUMIDITY 5000 41.2 24.90 14.230 (or water vapor density) is the ratio of the mass of water vapor to the total volume.
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