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Relative Humidity MINISTRY FOR THE ENVIRONMENT AND SPATIAL PLANNING SLOVENIAN ENVIRONMENT AGENCY REPUBLIC OF SLOVENIA Vojkova 1b, 1000 Ljubljana p.p. 2608, tel.: +386(0)1 478 40 00 fax.: +386(0)1 478 40 52 WMO CIMO Training Workshop on Metrology for the English-speaking countries of Region V (South-West Pacific) Melbourne, 21st - 25th November 2011 Relative humidity M.Sc. Drago Groselj Head of Calibration Laboratory Service 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Contents 9 Concepts and definitions 9 Introduction to measurement methods: dew-point, psychrometer, impendance themometer, mechanical 9 Humidity generators: Two-temperature, two-pressure, climatic chambers, salt solutions 9 Calibration tips…and traps 9 Humidity calculators 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Concepts and definitions Composition of air (by volume) Nitrogen Oxygen 78% 21% • Dalton’s law of partial pressures: total pressure can be expressed as other sum of partial pressures argon,CO ,... Water vapour ( 2 ) p = p + p + p + p UpUp toto 0.5%0.5% atat 00 °°CC total N2 O2 H2 0 other UpUp toto 4%4% atat 3030 °°CC 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Concepts and definitions 9 There are a number of ways of specifying humidity, as relative humidity RH (%), dew point DP (oC) or absolute humidity (g/m3). 9 Naturally they should all convert to the same humidity when compared. 9 The measurement of humidity is an attempt to find the partial pressure of water vapour. 9 The most fundamental standard is the gravimetric hygrometer. Certain amount of dry gas is weighed and compared with the weight of the test gas in the same volume (NIST, NPL, NRLM). 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Relative humidity • RH is the ratio of the actual water vapour pressure to the saturation water vapour pressure over a plane liquid water surface at the same temperature. • For the actual water vapour pressure e and the saturation water vapour pressure es , RH (in %) = e/es x 100 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Dew/frost point temperature ¾ The dew point (DP) is the temperature to which a humid air must be cooled for water vapour to condense into liquid water. This is the temperature at which air becomes saturated in equilibrium with water. In the range just below 0oC where either frost or dew (super cooled water) can form, the dew and the frost point differ. ¾ The frost point (FP) is the temperature at which frost forms on cooling a gas. This is the temperature at which air becomes saturated in equilibrium with ice. 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia ressurepCalculation of vapour A relatively simple equation for the calculation of the saturation vapour pressure ew(t) in the pure phase with respect to water is the Magnus formula (WMO): 17 .⋅t 62 100 243 .+t 12 90 (e )w t= 611 ⋅ . e 2 80 - range -45°C to 60°C / kaP 70 - e (t) [Pa] w w e 60 - t [°C] - uncertainty 0.6% of value 50 40 Saturation vapour pressure over ice: 30 22 .⋅t 46 20 e=611 .272 ⋅ e 2 .+t 62 10 i 0 - range -65°C to 0.01°C 10 30 50 70 90 - ei(t) [Pa] - t [°C] t / °C - uncertainty 1% of value 21st5 –2th November 2011 Traningi Workon Metrshop oogly, MeAuslbourne, tralia ressurepCalculation of vapour ¾ In literature are may expressions of saturated vapour pressure available but worldwide accepted Hardy formula based on ITS-90: ⎛ C1 2 ⎞ +C⎜ +2 C ⋅3 t + C 3 ⋅ t3ln( + C⎟ ⋅ ) t e() t= ⎝ et ⎠ - range 0°C ÷ 100°C w - uncertianty 0.005% of value ⎛ D ⎞ +D⎜ 1 + D ⋅ t + D2 ⋅ tln( + D⎟ ⋅ ) t - range -0100°C ÷ .01°C t 2 3 3 3 ⎝ ⎠ - uncertianty 0.5% of value e()i t= e where: ew() t o- saturation vapour pressure at temperature t ver water [Pa], - saturation ovapour pressure at temperature t ver ice [Pa], e()i t gi, ki - 1].constants available in literature [ 21st5 –2th November 2011 Traningi Workon Metrshop oogly, MeAuslbourne, tralia Conversion between DP/FP and RH ¾ There is no simple direct formula for converting in either direction between DP and RH. Conversions include the intermediate step of calculating the actual vapour pressure of water and the saturated vapour pressure of water at the temperature of interest. ⎛ ew ⎞ 243 . 12⋅ ⎜ ln ⎟ - range -45°C to 60°C 611⎝ ⎠ . 2 -e (t) [Pa] t = w d ⎛ e ⎞ - t [°C] 17 . 62− ⎜ lnw ⎟ - uncertainty 0.04°C 611⎝ ⎠ . 2 ⎛ e ⎞ 272 . 62⋅ ⎜ i ln ⎟ - range -65°C to 0.01°C 611 . 2 -e(t) [Pa] t = ⎝ ⎠ i f ⎛ e ⎞ - t [°C] 22 . 46− ⎜ lni ⎟ - uncertainty 0.08°C 611⎝ ⎠ . 2 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Water enhancement factor ¾ The “effective” saturation vapor pressure over water or ice in the presence of other gasses differs from ideal saturation vapor pressures. The effective saturation vapor pressure is related to ideal by: e(,)()() t p= e⋅ t f p f() p = enhancement factor −6 0 . 074 - Range -50°C to 60°C ( ) 1f .= p 0016 + 3 ⋅ . 15p ⋅ − 10 - p barometric pressure [kPa] p - uncertainty 0.08% of value The correction is small: approximately 2 parts per thousand! 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Water enhancement factor ¾ Latest Greenspan enhancement factor formula: 3 ⎡ ⎛ ⎞⎤ ⎛ es() t i ⎞ p α=A t ⋅i ⎢α⋅⎜1 − ⎟+β ⎜ ⋅ ⎟⎥ ∑ i f(,) t p= ⎣⎢ e⎝ p ⎠ ⎝es() t i ⎠⎦⎥ i=0 3 ln(β = ) ∑ Bi t ⋅i i=0 Ai, Bi - 1]constants available in literature [ The final formulae for relative humidity can be expressed as: e()(,) t⋅ f t p RH=100 ⋅ a a es()(,) t d/ f⋅ f t/ d f p 21st5 –2th November 2011 Traningi Workon Metrshop oogly, MeAuslbourne, tralia Effect of pressure ¾ ptotal = poxygen + pnitrogen + pwater + pothers ¾ For example what is the effect of doubling pressure on an RH of 40% at constant temperature? ¾ Since Ptotal has doubled, Pwater has doubled, and since T is constant the RH has doubled. i.e. RH = 80%. 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia The effect of temperature errors ¾ The effect of a 1oC error in temperature is shown in 7 graph. / % 6 ¾ Various ambient RH 5 Δ temperatures are plotted. 4 3 ¾ It can be seen that 1oC 2 error in temperature 1 0 90 10 50 determination equates to 20 30 10 RH / 50 about 5% error in RH for 70 % most temperatures. t / °C 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Classification of humidity instruments Typical Type Class Measurement range Measurement Accuracy Gravimetric hygrometer Primary -50°C ÷ 100°C 0.1°C dew point Chilled mirror Fundamental -90°C÷ 90°C dew point 0.2°C dew point hygrometer (transfer) 5% of reading Electrolytic hygrometer Fundamental 1 to 2000 ppmv ppmv 5% RH ÷ 95% RH Psychrometer Fundamental 1% - 5% RH 0°C÷ 100°C ambient Resistance hygrometer Secondary 5% RH-100% RH 1% - 5% RH Polymer RH sensor Secondary 5% RH -95% RH 2%-5% RH Mechanical hygrograph Secondary 10% RH-100% RH 2%-10% RH 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Introduction to measurement methods ¾ Condensation – dew point mirror ¾ Wet and Dry bulb - psychrometer ¾ Electrical impedance (resistance or capacitive) ¾ Mechanical - hygrograph 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Dew point mirror hygrometer ¾ The principle is simple, place a temperature controlled mirror in the air stream and cool it until dew forms on the mirror. ¾ This is a direct measurement of dew point. ¾ The temperature of the air stream is monitored and from these two measurements the other parameter can be calculated - RH. ¾ In operational systems such as the one shown the control of the mirror temperature is automatic. The thickness of the water layer is monitored with a reflected light beam irradiating a light detector. 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Dew point mirror hygrometer Advantage Disadvantage Uncertainty around 0.2°C Expensive Can provide precise Contamination can cause incorrect measurement readings Good long term performance Dew points below 0°C require careful interpretation Wide measurement range Can be slow in response 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Dew point mirror hygrometer ¾ Main uncertainty sources: - non-soluble contaminants on mirror surface - soluble contaminants on mirror surface ¾ Be careful: sometimes dew isn’t dew. The mirror should be monitored at dew points lower than 0°C to define either is a frost or dew point so the correct formula is used in RH calculation. Ice at –10°C Super cooled water at –11,1°C 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia RH valuef oCalculation Relative humidity is determined from dew/frost point measurements by following formula: e() t Where: s d/ f -e(t ) saturation vapor pressure at dew/frost point temperature t RH=100 ⋅ s d/f d/f -es(t a) saturation vapor pressure at air temperature ta es() t a If we include also water enhancement factors the final formula for dew point hygrometers become: e()(,) t⋅ f t p RH=100 s ⋅ d/ f/ d f e()(,)s t a⋅ f t a p Where: -es(t d/f) saturation vapor pressure at dew/frost point temperature td/f -es(t a) saturation vapor pressure at air temperature ta - f(td/f,p) enhancement factor at dew/frost point temperature td/f ( -fta,p) enhancement factor at air temperature ta 21st5 –2th November 2011 Traningi Workon Metrshop oogly, MeAuslbourne, tralia Expanded uncertainty of DP hygrometer 1.8 Uta = 0.08C 1.6 Utd/f = 0.1°C 1.4 Up = 50Pa 1.2 1 0.8 0.6 Expanded measurement uncertainty [%] [%] uncertainty measurement Expanded 0.4 0.2 0 10 20 30 40 50 60 70 80 90 100 Relative humidity [%] Ta = -20°C Ta = -10°C Ta = 0°C Ta = 10°C Ta = 20°C Ta = 30°C Ta = 40°C T 21st –25th November 2011 Training Workshop on Metrology, Melbourne, Australia Example Assume we have measured dewoint temperature -10/frost p°C, air temperature 20°aC nd air pressure 101.325kPa: - dew point temperature -10°C: ( 10esw− ) ° C = 286Pa .
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