Uncertainty Analysis in Humidity Measurements by the Psychrometer Method
Abstract
:1. Introduction
2. Theoretical Background
Equations for Determining Psychrometric Constant
3. Materials and Methods
3.1. Equipment
3.2. Sensors
3.3. Experimental Method
4. Results
4.1. Effect of Air Velocity on Tw
4.2. Comparison of Predictive Performance of Six Empirical Equations
4.3. Development of a New As Equation
R2 = 0.99483, s = 4.73762 × 10−5, Td > 30 °C,
4.4. Measurement Uncertainty of Humidity Calculated by Td and Tw Values
5. Conclusions
Supplementary Materials
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
A | psychrometric coefficient °C−1·kPa−1 |
As | psychrometric constant incorporated air atmosphere term, °C−1 |
e | vapor pressure, kPa |
es | saturated vapor pressure, kPa |
E | error of predictive performance, % |
Emax | maximum error of predictive performance, % |
Emin | minima error of predictive performance, % |
absolute error of predictive performance, % | |
ave | average of |
n | number of data |
P | atmosphere air pressure, kPa |
RHcal | calculated RH value from empirical equation |
RHsta | standard RH value from ASHRAE Handbook |
T | temperature of air, °C |
Td | dry bulb temperature, °C |
Tw | wet bulb temperature, °C |
u(RH) | uncertainty of relative humidity |
u(Td) | uncertainty of dry bulb temperature |
u(Tw) | uncertainty of wet bulb temperature |
Appendix A. Evaluation of the Measurement Uncertainty
- 1
- Model the measurementy is not measured directly and is determined from K quantities ,The functional relationship is as follows:
- 2
- Ensure the uncertainty source and calculate the estimated values of
- 3
- Evaluate the uncertainty classified as A and B types.
- 4
- Estimate the covariance of each .
- 5
- Calculate the sensitivity coefficient,
- 6
- Calculate the combining uncertainty and effective degree of freedom.
- 7
- Determine a coverage factor and expanded uncertainty.
- 8
- Report the uncertainty.The uncertainty of RH value that calculated from Td and Tw values.By Equation (A2), the uncertainty of RH can be calculated follows:If As is a constant,If ,
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1 | Penman equation [22] |
Pw = Pws (Tw) − 0.0664 × (Td – Tw) | |
2 | Goft-Cratch equation [23] |
Pw = Pws (Tw) − 0.067193 × (Td – Tw) | |
3 | British United Turkeys (BUT) equation [24] |
Pw = Pws (Tw) − 0.066 × (Td – Tw) | |
4 | Harrison equation [25] |
Pw = Pws (Tw) − 0.067 × (1 + 0.00115Tw) × (Td – Tw) | |
5 | World meteorological Organisation (WMO) equation [26] |
Pw = Pws (Tw) − 0.0662795 × (1 + 0.000944Tw) × (Td – Tw) | |
6 | Nevia et al. equation [27] |
Pw = Pws (Tw) − 0.0647164 × (1 + 0.00504Tw) × (Td – Tw) |
Temp. (°C) | Criteria | As (This Study) °C−1 | Penman | BUT | Goff-Cratch | Harrison | WMO | Neiva et al. |
---|---|---|---|---|---|---|---|---|
15 | Emin | −0.0032 | 0.0278 | 0.0336 | 0.0510 | 0.2783 | 0.0508 | 0.1171 |
Emax | 0.0476 | 0.5321 | 0.6259 | 0.1041 | 0.9483 | 0.6808 | 0.8323 | |
ave | 0.0988 | 0.2261 | 0.2691 | 0.3966 | 0.6492 | 0.3331 | 0.5575 | |
20 | Emin | −0.00823 | 0.1999 | 0.0115 | 0.0370 | 0.2353 | 0.0435 | 0.1200 |
Emax | 0.0300 | 0.4577 | 0.2866 | 0.7969 | 0.9548 | 0.6735 | 1.3476 | |
ave | 0.0079 | 0.1917 | 0.1947 | 0.3443 | 0.6330 | 0.3332 | 0.7268 | |
25 | Emin | −0.0090 | 0.0164 | 0.0195 | 0.0289 | 0.0557 | 0.0387 | 0.1161 |
Emax | 0.0056 | 0.3528 | 0.4223 | 0.6282 | 0.9358 | 0.6150 | 1.3540 | |
ave | 0.0448 | 0.1531 | 0.1841 | 0.2759 | 0.4612 | 0.3091 | 0.8033 | |
27.5 | Emin | −0.0018 | 0.0156 | 0.0183 | 0.0264 | 0.2815 | 0.0370 | 0.1126 |
Emax | 0.0051 | 0.3161 | 0.3187 | 0.5645 | 0.9617 | 0.5918 | 1.4235 | |
ave | 0.0029 | 0.1418 | 0.1696 | 0.2523 | 0.6542 | 0.3016 | 0.8282 | |
30 | Emin | −0.0423 | 0.0153 | 0.0176 | 0.0246 | 0.2474 | 0.0356 | 0.1080 |
Emax | 0.0054 | 0.3132 | 0.3745 | 0.5562 | 0.9635 | 0.6021 | 1.4964 | |
ave | 0.0058 | 0.1422 | 0.1693 | 0.2494 | 0.6368 | 0.3205 | 0.8774 | |
32.5 | Emin | −0.0069 | 0.0153 | 0.0174 | 0.0234 | 0.2603 | 0.0346 | 0.1048 |
Emax | 0.0056 | 0.2870 | 0.3423 | 0.5060 | 0.9651 | 0.5818 | 1.5331 | |
ave | 0.0024 | 0.1384 | 0.1628 | 0.2349 | 0.6418 | 0.3068 | 0.8004 | |
35 | Emin | −0.0015 | 0.0156 | 0.0174 | 0.0267 | 0.2715 | 0.0338 | 0.1008 |
Emax | 0.0057 | 0.2679 | 0.3119 | 0.4654 | 0.9665 | 0.5649 | 1.5543 | |
ave | 0.00216 | 0.1576 | 0.1576 | 0.2224 | 0.6474 | 0.3015 | 0.8851 | |
40 | Emin | −0.0030 | 0.0170 | 0.0183 | 0.0223 | 0.0411 | 0.0329 | 0.0929 |
Emax | 0.0057 | 0.2470 | 0.2877 | 0.4083 | 0.7609 | 0.5406 | 1.5631 | |
ave | 0.0024 | 0.1388 | 0.1566 | 0.2095 | 0.4017 | 0.3015 | 0.8751 | |
45 | Emin | −0.0020 | 0.0188 | 0.0199 | 0.0230 | 0.0399 | 0.0327 | 0.0858 |
Emax | 0.0034 | 0.2444 | 0.2778 | 0.3768 | 0.7177 | 0.5271 | 1.5428 | |
ave | 0.0011 | 0.1511 | 0.1656 | 0.2088 | 0.3910 | 0.3016 | 0.8592 | |
50 | Emin | −0.0076 | 0.0210 | 0.0218 | 0.0242 | 0.0389 | 0.0331 | 0.0797 |
Emax | 0.0077 | 0.2568 | 0.2859 | 0.3725 | 0.7041 | 0.5313 | 1.5342 | |
ave | 0.0046 | 0.1719 | 0.1848 | 0.2232 | 0.4015 | 0.3190 | 0.8706 |
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Chen, J.; Chen, C. Uncertainty Analysis in Humidity Measurements by the Psychrometer Method. Sensors 2017, 17, 368. https://doi.org/10.3390/s17020368
Chen J, Chen C. Uncertainty Analysis in Humidity Measurements by the Psychrometer Method. Sensors. 2017; 17(2):368. https://doi.org/10.3390/s17020368
Chicago/Turabian StyleChen, Jiunyuan, and Chiachung Chen. 2017. "Uncertainty Analysis in Humidity Measurements by the Psychrometer Method" Sensors 17, no. 2: 368. https://doi.org/10.3390/s17020368
APA StyleChen, J., & Chen, C. (2017). Uncertainty Analysis in Humidity Measurements by the Psychrometer Method. Sensors, 17(2), 368. https://doi.org/10.3390/s17020368