1995 - an error analysis of … to “swing” a sling type psychrometer in a humidity chamber. in...

AN ERROR ANALYSIS OF PSYCHROMETERS

Presented by: Jeff Gust, Metrology TechnicianGTE Equipment Repair Services

2970 Inland Empire Blvd.Ontario, CA 91764

Work (909) 945-0347FAX (909) 945-5664

Author: Jeff Gust

ABSTRACT:

Psychrometer are well established as an acceptable method of performing humiditymeasurements, and are potentially dependable in obtaining accurate measurement results.Due to the complexity of the mathematics, however, difficulties may arise in the relation ofthermometer temperature measurement error to the resulting error in relative humidity.This presentation revisits the algorithms for humidity determination, employing easy-to-use electronic mathematical worksheet programs available for personal computers. Totaluncertain y of measurement in the thermometer calibration is calculated in accordancewith the document 1S0 TAG 4, “The Guide to Expressing Uncertainty in Measurement .“A brief discussion of humidity terms and concepts is also included.

INTRODUCTION:

The American manufacturing industry continues to adopt new quality and safety standardsas international pressure for standardization and consumer demand for quality goodsincreases. Humidity and other environmental parameters which were not previouslymonitored are now coming under intense scrutiny, thus the measurement and control ofhumidity is becoming commonplace in many industrial facilities.

Humidity directly impacts the safety and efficiency of many industrial and manufacturingprocesses. Water content of air must be monitored, as either too much or too littlehumidity can sabotage routine operations. For example, without proper humidity control,static charges can cause damage to circuit boards during manufacturing and testingprocesses. In addition, low humidity and static charge present an increased explosionhazard in areas where fine dust or powder is present. In the textile industry, the operationof fabric processing can be impeded by the repulsion and attraction of fabrics due to staticcharge. On the other end of the continuum, excessive humidity will damage virtually anytype of stored material via decay, mold or rust.

1995 N(XL Workshop & Symposium 583 Session 7C

The scope of this discussion will cover the definition of humidity and the flmdamentals ofhumidity measurement. The calibration of psychrometer with liquid-in-glassthermometers as indicating devices, defining the uncertainty of calibration in accordancewith ISO TAG 4, “The Guide to Expressing Uncertainty in Measurement,” will also beexamined. Also included is a discussion of sources of potential error in psychometricmeasurement.

BASIC HUMIDITY CONCEPTS:

The American Heritage Dictionary defines humidity as: ahmpness, eWecialIy of air. It isthe metrologist’s goal to measure the amount of “dampness” that is actually present in air.

Air is composed of number of different gases including water vapor, which is water in thegaseous phase. In order to expedite this discussio~ air will be considered to have onlytwo components: water vapor, and all other dry gasses. Dalton’s Law states that the totalpressure of a gas mixture is the sum of the partial pressures of each of its components.Therefore, humidity itself is measured by measuring the partial pressure of water vapor asa component of atmospheric pressure, which is approximately 760 millimeters of mercuryabsolute at sea level.

When considering and measuring humidity, it is important to remember that there is amaximum amount of water vapor that air can hold. That is, the partial pressure of watervapor in an air sample for a given temperature cannot rise above a certain value. Theamount of water vapor that can actually be held in air is dependent on temperature. Atlower temperatures, very little water vapor can be held in air, and the partial pressure ofwater vapor is small. At higher temperatures up to and including the boiling point ofwater, the amount of water vapor in air and the partial pressure of water vapor increase.At the boiling point of water, the partial pressure of water vapor exceeds atmosphericpressure. The air has reached the maximum water vapor that it can hold, and the excess iscondensed into water and seen as steam.

1995 NCSL Workshop & Symposium 584 Session 7C

760 mm Hg

4.6 mm Hg

L

; DRY GAS

t

al :

WATER VAPOR i

,

Oc tl temperature in deg C t2 100c

FIG. 1, WATER VAPOR PRESSURE AS A FUNCTION OF TEMPERATURE

In Figure 1, the’curve represents magnitude of water vapor saturation pressure as afimction of temperature. Notice at temperature t 1 that the water vapor saturation pressureb 1 is a small component of the 760 millimeter atmospheric pressure, and that the dry gaspartial pressure makes up the largest part. At temperature t2, the quantities a2 and b2have reversed. At zero degrees Celsius there still exists a vapor saturation pressure. Attemperatures below zero degrees Celsius this water vapor saturation pressure is caused bya transition directly from ice to water vapor. For the scope of this discussion, humiditymeasurements below the ileezing point of water will be omitted.

WATER VAPOR PRESSURE VS. WATER SATURATION PRESSURE

At this time it is important to note that the curve represented in Figure 1 is the maximumpressure that can be achieved by water vapor at a specific temperature. This is alsoreferred to as saturation pressure of water vapor. The actual amount of water in air orwater vapor pressure can vary from zero up to the saturation pressure.

HUMIDITY TERMS DEFINED

At the saturation pressure of water vapor for a given temperature, water is eitherevaporated to a gas, or is condensed from gas to water. This point is refereed to as thea?ewpoint for a given temperature. Certain humidity measurements find the amount ofwater vapor for a given temperature by reducing the temperature of the gas until a dew isformed, and state that temperature as the dew point. For example, when the temperaturedrops, the amount of water the air can hold is decreased, and if more water vapor is


present in the air than the air may hold for a given temperature, the excess water vapor iscondensed into dew or rain.

Another type of humidity measurement is made by determining the water vapor pressureof a gas at a specific temperature, then finding the saturation pressure for thattemperature, usually from a calculated chart. The water vapor pressure is then divided bythe saturation pressure and multiplied by 100 to find the percentage of relative humidity.

vapor_ pressurerelative_ humidity = x 100

saturation_ pressure(1)

If the water vapor pressure equals the saturation pressure then the relative humidity is 100percent for that given temperature. Note that the same water vapor pressure at giventemperatures will result in different percentages of relative humidity.

760

s’E 28.3E

4.6

. .......................

DRY GAS

saturation pressure of sample----- ------ ------ ------ ------ ------ ------ .-. -.—._._._._._._._.

vapor pressure of sample----- ------ ------ ------ ------ .—.—._.—._,_._._._ :“-”-”-“---”—-,

WATER VAPOR

Oc temperature in deg C 20 28 100C

FIG. 2, HUMIDITY MEASUREMENT AT 28 DEGREES C

Example:

The humidity of a gas sample with a temperature of 28 degrees C is measured by loweringthe temperature of the gas until dew appears. The gas temperature when dew first appearsis 20 degrees C. Using a reference table it is determined that the saturation pressure at 28

1995 AJCSL Workshop & Symposium 586 Session 7C

degrees C is 28.3 mm H~ and the saturation pressure at 20 degrees is 17.5 mm Hg.Applying this data to equation (1) yields:

The dew point of the gas sample is 20 degreesThe relative humidity of the gas sample is:

17.5mmHgx 100 = 61.8°/oR.H.

28.3mmHg

THEORY OF OPERATION OF THE PSYCHROMETER

The principles of humidity measurement are derived directly from mechanical,thermodynamic, and electrodynamicsproperties of physics and chemistry, One of theoldest and most accepted methods of measuring humidity is the use of a psychrometer. In1825, Henri Regnault, a French scientist, observed that when a piece of muslin wasmoistened with water and exposed to the atmosphere, evaporation accompanied bycooling generally occurred. If the muslin was wrapped around a thermometer, anindication of the cooled temperature could be observed. Regnault theorized that theamount of cooling was dependent on the hydrometric state of the atmosphere, and indoing so assembled the first psychrometer. A psychrometer generally consists of twothermometers with matched temperature scales. The thermometers are placed side byside, and a cotton sleeve is fitted over the bulb of one thermometer. The cotton sleeve issoaked with distilled water. An airflow is generated over the thermometers by eitherphysically swinging the psychrometer in the air or having a motor circulate air over boththermometers. The bulb of the wet thermometer cools due to evaporation of water fromthe surface of the bulb until a thermal equilibrium is achieved. The temperatures of thewet and dry bulb are then recorded. Given the proper measurement charts (refer to figure3), a technician with little training can obtain humidity measurements with little or noknowledge of humidity principles.

Problems begin to arise, however, in the calibration of the psychrometer. Most humidityinstruments are calibrated in a two pressure humidity chamber, but there is not enoughspace to “swing” a sling type psychrometer in a humidity chamber. In additio~ specialtooling usually not available to the technician maybe necessary to ensure adequate airflow over the thermometers while in the humidity chamber. Since the largest contributorof psychrometer error is due to inaccuracies of the thermometer, the way to determine theaccuracy of a psychrometer is to remove its thermometers and calibrate them in atemperature bath. It is then necess~ to convert the calibration accuracy of thermometersback to a relative humidity representation. In order to make a conversion fromtemperature depression of the wet bulb to a relative humidity measurement, themetrologist must understand certain concepts of humidity measurement.

DETERMINATION OF VAPOR PRESSURE AND SATURATION PRESSURE

Now that terms of humidity such as water vapor pressure and saturation pressure havebeen defined, pressures from data taken by the psychrometer can be calculated. Reference


CMfFtR[NCf BfTWftN DRY.8ULI AND WT4LU IfAWRAIURff,t.

2

ii

v v I I I I I I i I i 1 I I [ 1 I I IAA I

8

DmBe4a BETwfENmr.u.al AM) WmBIN.I nA4FQAnJufs.7

Fig. 3, Percentage of Relative Humidity vs. Wet-bulb and Dry-bulb TemperatureDifference, Temperature Range, Oto 80 degrees F; Pressure 760 mmHg


tables can be employed to find these partial pressures, but most tables only have 1 degreeresolution at best, leaving the metrologist to interpolate between integer degrees. Othercommon instruments or charts include calibration curves as in figure 3, or sliding scales,which can introduce errors if one incorrectly reads the scale or curve. Interpolation errorcan also occur.

Despite the perceived conveniences and efllcacies of tables and charts, the most accurateand reliable way to determine relative humidity using a psychrometer is by directcalculation. Direct calculation affords the metrologist direct control of the accuracy ofnumeric values and calculations, resulting in a more precise measurement. The formulafor relative humidity is:

R. H.=+x1OOWST

(2)

where:R.H. = Relative Humidity in percentPW = the partial pressure quantity of water vapor pressure in the atmosphere in Pascals

Pm= the partial pressure quantity of vapor saturation pressure at dry bulb (atmospheric)

temperature in Pascals

Note that the division of equation (2) yields a ratio which is converted to a percentage bymultiplying by 100. Also note that relative humidity is a dimensionless number due to theunit quantities that cancel out by division.

Expanding upon the equation for relative humidity, the formula for vapor saturationpressure at the dry bulb temperature (which must be greater than Odeg C) is:

Pwm = eB’ (3)

This equation states that the dry bulb vapor saturation pressure equals the naturalexponential fhnction to the B 1 power. The term B 1 of equation (3) is defined as:

B1 = [($) + C9 + cl,~d +Cl,~l + c,,~j + %(ML))l (4)d

where:~ = the temperature of at the dry bulb

Constants C8 through C,~ are constants to describe a best fit to the curve of dry bulb

temperature versus water vapor saturation pressure. The numerical values for theconstants as defined by ASHRAE standard 41.6- 1982R are as follow:

C8 = 5.8002206X 103 c, =1.3914993 C,O = -4.8640239X 10-2


Cl} = 4.1764768X 10-5 C,2=1.4452093X 10-8 C,, = 6.5459673

The equation for determining the quantity of water vapor pressure in the atmosphere is:

(5)

where:PW = the partial pressure of water vapor saturation at the wet bulb in Pascals

A= the psychrometer coefficient (sometimes stated by the manufacturer. If coefficientis not stated, as was the case for this paper, the value of the coefficient is6.7 X 10AK-’)

~= temperature recorded at the dry bulb

Tw = temperature recorded at the wet bulbp. The absolute air pressure measurement in Pascals

The last part of the relative humidity equation is the calculation of water vapor saturationat the wet bulb which is:

Pw, = eB3 (6)

and the term B3 of equation (6) is defined as:

B3 = [($) + C9 + CIOTW+ C,,Tj +C,2T~+C,3(ln(Tw))] (7)w

Equation (6) is nearly identical to the determination of the vapor saturation pressure at thedry bulb, equation (3). The only difference in equation (6) is that the temperature is therecorded temperature of the wet bulb.

The complexity of the equations and required calculations demonstrate the reason thatcharts were derived for use with the psychrometer. The determination of relative humidityfrom wet and dry bulb measurements via lengthy, manual calculations is both diflicult andtime consuming. Such calculations are impractical and have and increased chance oferror, thus making reliance on a chart a fairly practical, if inaccurate, option.

However, with the aid of a computer or advanced calculator, these equations andcalculations can be expediently computed yielding much more accurate and reliablemeasurements than the charts. Advances in computing technology provide an opportunityto properly utilize humidity-determining calculations, free of human errors inherent inmassive, complex mathematics and interpolation from charts. Fortunately, nearly everymetrologist today has easy access to a personal computer or programmable scientificcalculator. The formulas used to calculate relative humidity can be employed as anexecutable program or through various mathematical electronic worksheets. In the nextexample, the program Mathcad 5.0 was used for calculation of relative humidity.


WORKSHEET FOR CALCULATINGRELATIVE HUMIDITYOF PSYCHROMETERSBY MEASURINGTEMPERATURE DEPRESSION

OF WET BULB VS. DRY BULBTw~.’16 temperature of wet bulb in deg C

Td~ :=20 temperature of dry bulb in deg C

P :=97928 absolute air pressure measurement in pascals

A :=6.7.10-4 psychrometer coefllcient (use 6.7 if none stated)

determination of saturation partial pressure at the wet bulb

TW:=TW1+273.15 conversion of wet bulb temperature from C to K

Td :=Td*+273.15 conversion of dry bulb temperature from C to K

C 8 :=-5.80022061(? Cg := 1.3914993 C lo :=-4.864023910-2

C ~1 :=4.176476810-5 C 12 :=- 1.445209310-8 C 13 := 6.5459673

[()C*B3 := – +c,+(cl~Tw)+(cllT~)+(c12T~Tw )+(%%))]

P B3~ :.e formula for saturation partial pressure at the wet bulb

[()C*B1 :. — +Cg+(Cl@d)+(cll” Td

Td 2)+(c12T~)+ W(w)]

P BIWst :=e

formula for saturation partial pressure of water vapor atdry bulb

Pw:=Pws - A.(Tdl - Twl).p formula for partial pressure of water vaporin the atmosphere

PwRH := loo— formula for relative humidity

P Wst

RH = 66.529 calculated relative humidity


At this point, an electronic worksheet has been created that can calculate relative humidityfrom psychrometer temperature depression. Using the Mathcad software, the actualmathematical computations can be presented in the same manner that they are developedin a theoretical text. This type of format is easy for an end user such as a customer toread. In addition, if the customer is ftiliar with the mathematics, it is immediatelyapparent that the calculations are sound, as opposed to the inconvenience of decipheringprogramming code. For companies involved in ISO 9000 certification, software is auditedfor accuracy of results. The example presented in this worksheet is extremely easy toveri& for accuracy.

The program Mathcad is available in various platforms, including Windows, Macintosh,and UNIX, so that nearly any system can utilize this sofiware package. When a techniciantakes a humidity measurement, instead of looking up dry bulb temperature and wet bulbdepression on a table and then interpolating from a curve, this electronic worksheet can beemployed, a more precise calculation obtained, and complete results (with a worksheet)printed.

ESTIMATING THE ERROR OF A PSYCHROMETER CALIBRATION

The theory of operation of psychrometer has been identified and analyzed. The next taskis to calibrate the psychrometer. This includes the potentially arduous task of estimatingthe accuracy of the psychrometer and calculating the total uncertainty of measurement inthe calibration.

CALIBRATION OF THE PSYCHROMETER

The psychrometer is calibrated by disassembling the unit, removing the thermometers, andcalibrating the thermometers as standard liquid-in-glass thermometers. Each thermometeris calibrated by immersion into a liquid temperature bath. The reference thermometer is adigital resistance temperature detector @TD) thermometer has a manufacturer specifiedaccuracy of+/- a.

In the following example, data is taken at n=II temperature readings tk of thethermometer, with corresponding known reference temperatures tR,kin the temperature

range of the thermometer under test to obtain the corrections b~ = t~,~ – t~ to the

readings. The measured corrections b~ and measured temperatures tk are the input

quantities of the evaluation. A linear calibration curve

b(t)=y, +Yz(f - L) (7)

is fitted to the measured corrections and temperatures by the method of least squares. Theparameters y, and yz, defined respectively as the y-intercept and the slope of thecalibration curve, are the two output quantities to be calculated. The temperature 10is aconveniently chosen exact reference temperature, usually the lowest temperature


measurable by the thermometer under test. once yl and Y2 ~e found, along with theirvariances and covariance, the linear equation can be used to predict the calibration offsetand standard uncertainty of the correction to be applied to the thermometer for any value tof the temperature. The following set of equations are used to determine the y-intercepty] and its standard uncertainty s(y,), the slope y, and its standard uncertainty S(yz), thecorrelation coefficient r(yl, y2 ), and the pooled sample standard deviation S.

The expanded uncertainty of measurement is defined by 1S0 Tag 4 as the quadratic sumof the type A or random error (not to be confbsed with psychrometer coefficient A), andthe type B or standards error. This quadratic sum is then multiplied by a coverage factorK, in order to obtain an expanded uncertainty.

(8)

where:Ui = the type A uncertaintyuj = the type B uncertainty

K = the coverage factor

The type A evaluation of standard uncertainty for the following example is the pooledstandard deviations of the linear equation. The type B uncertain y is derived fi-omcalculating the standard deviation of the digital RTD thermometer. There is no additionalspecific knowledge regarding the accuracy of the digital RTD thermometer in thisexample. It is assumed that the manufacturers specifications assumes a 100 percentprobability of lying between the bounds of a+ and a- in this example, therefore theformula for the standard deviation is:

/

a=Uj. —

3(9)

The value of the coverage factor K is typically in the range of 2 to 3, which corresponds tohaving a level of confidence from 95 to 99 percent in the combined standard uncertainty.

The calibration standard used is a digital RTD thermometer with a manufacturers statedaccuracy of a=+/- 50 mK. By using the manufacturers specifications for the digital RTDthermometer and equation (9) the calculated type B uncertainty is 29 mK.

The equations shown below are taken from a Mathcad worksheet that not only displaysthe equations of a linear curve, but will simultaneously calculate the curve for thecalibration data entered.


WORKSHEET FOR CALCULATING SLOPE ANDOFFSETS OF LIQUID AND GLASS THERMOMETERCALIBRATION

n:= 11 number of data test points taken

k:=l.. nt,,=

!1.5212.0122.5123.0033.5073.9994.5135.0025.5036.0106.511

to:=20

test data taken for unit under test

tRk :=test data taken for calibration standard

H1.350 bk:=t Rk-tk1.843

H2.3462.8443.343

H3.8344.3574.845

bk

-0.171

-0.169

-0.166

-0.159

-0.164

-0.165

-0.156

-0.157

-0.159

- 0.161

-0.16

observed corrections for each data point

reference temperature, beginning of linear equation

ek:=tk -to

D := n. 20ek2-k=]

n 2

‘)

ek

k=l

Y1 ‘_O.1712

1995 NCSL Workshop

D

calculated y intercept

& Symposium 594 Session 7C

,,.n”i$lbk”ek-(izb—D

y 2 = 0.002183 calculated slope of the best fit line

b\:=y1+y2&t~)

b+K

h -i

l+-0.1679

-0.1668

-0.1657

m

i

-0.1635

-0.1625

-0.1614

-0.1603

-0.1592

-0.1581

-0.157

~ (’k-’t,)’

s ,= ‘=1

4 n–2

()SY1 = 0.0029


rS(Y2) . :2

S (y ~) = 6.67910-4

n

z ok

‘(YA ‘=-’”,&--In

Inz (’k)’

‘(YI3Y2)‘+-93043


CALIBRATION REPORT FOR LIQUID IN GLASS THERMOMETERS

CALIBRATIONSTANDARDSMEASUREMENTS

tR

21.35

21.843

22.346

22.844

23.343

23.834

24.357

24.845

25.344

25.849

26.351

UNIT UNDERTEST RECORDEDMEASUREMENTS

t

R21.521

22.012

]22.512 I

123.003 I

El23.507

23.999

24.513

25.002

25.503

Id26.01

26.511

Calculations using calibration data to generate least squares fit of linear cume of the form:

B(T) :=y1+y2. (T-to)

B(T)

y~ =-0.171

y z = 0.00218

to =20

()s Y1 = 0.0029

s (Y2) = 6.67910-4

r(Yl>Y2) ‘4.93

s = 0.0035

a = .050

k=2

[

a2

‘.i “= —

Ju ,= k. S2+uj2

U = 0.058

1995 NCSL Workshop

the observed temperature correction for temperature T

y intercept of line

slope of line

lowest temperature measurable by this thermometer

standard deviation of the y-intercept

standard deviation of the slope

correlation coefllcient of the slope and y-intercept

pooled sample standard deviation

Enter here the manufacturer accuracy specificationof the standard thermometerEnter here the coverage factor for the evaluation

equation for estimating the standard deviation of thestandard thermometer

equation for total uncertainty of thermometer calibration

expanded uncertainty of thermometer calibration in degrees C

& Symposium 597 Session 7C

THE RELATION OF THERMOMETER ERROR TO THE PSYCHROMETERMEASUREMENT

Now that the uncertainty of the thermometer calibration has been determined, this valuecan be used to find the resulting error in relative humidity. The relative humiditydetermination varies widely due to the dry bulb temperature and the temperaturedepression of the wet bulb. Thus, the resulting error propagation due to the thermometercalibration varies greatly, and it is not reasonable or accurate to assign a fixed uncertaintyto the psychrometer from the thermometer error.

An additional advantage available by using electronic worksheets is that these worksheetscan be easily modified for similar fhnctions. At this point, the previous worksheet can bemodified to make a program that incorporates calibration error of the thermometer intothe original equation and analyze it for individual points. Additionally, error graphs can beproduced to examine the effect of calibration error across a broad spectrum ofmeasurement. Since the electronic worksheet used was oriented for use in Windows,editing fi.mctionswere available such as “cut” and “paste.” Therefore, the time required tocreate each new worksheet was approximately 15 minutes.

1995 IVCSL Workshop & Symposium 598 Session 7C

WORKSHEET FOR CALCULATING RELATIVE HUMIDITY ERROROF PSYCI-IROMETERS BY MEASURING TEMPERATURE DEPRESSION

OF WET BULB VS. DRY BULB

Twl = 14 temperature of wet bulb in deg C

Td~ =20 temperature of dry bulb in deg C

P = 97928 absolute air pressure measurement in pascals

A = 6.7.104 psychrometer coefficient (use 6.7 if none stated)

TW2 =.1 calibration error of wet bulb thermometer in deg C (enter Oif none)

Td2:=-.lcalibration error of dry bulb thermometer in deg C (enter Oif none)

Determination of saturation partial pressures at the wet bulb

T w:= T WI + 273.15conversion of wet bulb temperature from C to K

T d :=T dl + 273.15 conversion of dry bulb temperature from C to K

T we:= T w + T Wz adding in wet bulb error into calculations

Tde:’Td+Td~ adding dry bulb error into calculations

curve constants:

C ~ :=- 5.80022061& c g :=1.3914993 C 10 :=-4.8640239102

C ~1 :=4.1764768105 C 12 :=-1.4452093108 C *3 :=6.545%73

1()C*B3 ,= —

( )(+Cg+ CIO”TW + C1l” TW2

Tw )+(C 12TW’)+ (c 131n(Tw))]

PB3

Ws ❑ e formula for saturation partial pressure at the wet bulb

[()cj3B3e :. — ( )(+Cg+ Clo” Twe + C11Twe2

T + c 12”TW:) + (c 13”1n(Twe)))(we

PB3e

wse’= e formula for determining error in wet bulb saturation pressure

[[1C$jB1 ,. — +C9+ (c @’d) + (cll”T/)+(c12”Td3) + (c 13”ln(Td))

Td1


.

PB1

Wst ‘= e formula for saturation partial pressure of water vapor atdry bulb

[()cf3Bl~ ,. — ‘c9+(c10-Tde)+(cll-Tde2

Tde)(

+ C ~~Td~)+(c 13-ln(Tde))]

PBle

wste := e formula for error in saturation pressure at the dry bulb

Pw:=pws - A“(T dl - T w 1) “P formula for partial pressure of water vaporin the atmosphere

P -P( )

-A. Tde-Twe “pwe :- wse

Pw~ :. lo(_).—

P Wst

RH = 51.522

Pme :.100. ‘e

P wste

RFle = 52.855

RHe - RH = 1.333

formula for relative humidity

calculated relative humidity

formula for relative humidity using calibration error offsets

calculated relative humidity with calibration error offsets

deviation between calculations using direct reading of thermometers

and calculations using cfllbration offsets.


Error: wet bulb +.25 deg, dry bulb +.25 deg

3

2.5

0

/-’

/’

.....-......... ...-’’”””

/,/.-.

...-

. -------._, -./

......... ------

I

2 4 6 8 10 12 14 16 18 20

WET BULB DEPRESSIONJNDEGREESC

— @bulb temp5degC-----drybulbtemp15degC‘- @ bulbtemp20&g C‘“- &ybulbtemp25degC— drybulbtemp35degC

Fig. 4, Humidity error resulting from calibration of the thermometers


Error: wet bulb +.25 de~ dry bulb Odeg

4

3.5 ‘ \

g

# 3 ‘\

x?

-

d

8~ 2.s ‘-”’”’” .......

........$ .......

g ---+-.-%....,.,..

.-............

............-.gz * “---- ::.-:’ “---- .h+ti ~+ ......

...“------ - ““’-.. ............ ....

3-- ...............-.-.-.x, ---

$ 1“’

=\ ------ . -’-. ___“------- -----

a

----.-. _ —---------------- ._

1

0.52 4 6 8 10 12 14 16 18 20

WET BULB DEPRESSIONIN DEGREESC

— drybulbtemp5&g C-“ drybulb hp 15 &g C‘- dxybulbtemp20&g C‘- chybulbtemp25deg C— dry bulb temp 35 (leg C



Error: wet bulb +.25 deg, dry bulb -.25 deg

,2 4 6 8 10 12 14 16 18 20

WET BULB DEPRESSIONIN DEGREESC

— dry bulb temp 5 &g C-- dry bulb temp 15 deg C‘– dry bulb temp 20 deg C‘-- dry bulbtemp25deg C— dry bulb temp 35 deg C


OTHER POTENTIAL SOURCES OF PSYCHROMETER ERROR

At this time, psychrometer measurement error due to thermometer error has beenthoroughly discussed. However, error due to other factors in the equation of relativehumidity with a psychrometer must also be considered. The following examples providedare calculated for a one point measurement, but like relative humidity error propagationresulting from thermometer error, the results of these potential sources of error varywidely with respect to d~ bulb temperature and wet bulb depression.

The Psychrometer Coefficient

In accordance with the ASHRAE standard 41.6-1982~ the psychrometer coefficient A isto be a set value between 6.5x 10A and 6.9x 10A K-l. If the value of A has beendetermined to be within this range, it shall be used. If the value of A is outside of thisrange, the closest of the extreme values are to be used.

Using the Mathcad worksheet for calculating relative humidity, the value of A can bechanged and the resulting error of humidity measurement can be calculated. As an


example, for a dry bulb temperature of 20 degrees and a wet bulb temperature of 15degrees, varying the psychrometer coefficient A between 6.5x 10q to 6.9x 10q K-’ theresulting deviation in the relative humidity calculation is .838°/0

This potential error involving the psychrometer coefficient is relatively small incomparison to thermometer error, however, it is critical to consider when determiningpsychrometer accuracy.

Air Pressure

Air pressure is also taken into consideration when calculating the partial pressure of watervapor in the atmosphere. As was the case for the psychrometer coefficient ~ theMathcad worksheet can be employed to change the value of air pressure to analyze thepotential for error in the calculation of relative humidity.

As an example, for a dry bulb temperature of 20 degrees C and a wet bulb temperature of15 degrees C, changing the air pressure from 101325 Pascals (760 mmHg) to 97325Pascals (730 mmHg) the resulting deviation in relative humidity is .573V0. Thepsychometric tables that are most commonly used today assume an air pressure of101325 Pascals.

As there are very few locations in the United States that have an average air pressure of101325 Pascals, an additional error is inherently propagated into the measurement ofrelative humidity.

MISCELLANEOUS CONSIDERATIONS

The technician using the psychrometer should be aware of other conditions that may affectthe accuracy of the humidity measurement. These conditions are assumed to cause onlysmall to insignificant error. I have not found any reports that quanti~ the error caused bythese conditions at this time, but as these conditions cause error, they must be consideredand evaluated.

Radiation shields with transverse ventilation can be attached to the psychrometer toreduce the amount of extraneous thermal radiation upon the thermometers.

In accordance with ASHRAE specifications, airflow over both the wet and dry bulbs shallbe a forced flow of 4 +/- 1 rrds for transverse ventilation and 2 +/- .5 m/s for axialventilation. The importance of a good airflow is to cool the wet bulb by enthalpy of waterevaporation. If the airflow is too high, such as swinging a sling psychrometer too fast, thewet bulb will only cool until it reaches and equilibrium with the water vapor in the air, sothis is not necessarily a detrimental condition. However, if the airflow is too low, anequilibrium of the wet bulb vapor and atmospheric water vapor will not be achieved. Thiswill result in errors in determining relative humidity of the air,


The water used on the wet bulb must be of a high quality, preferably distilled. Watercontamination will result in changing the wet bulb depression due to a different enthalpy ofvaporization.

The makeup and condition of the wick over the wet bulb must be noted as well. Themanufacturer usually specifies the type of wick for their psychrometer, Care must betaken to ensure that the wick is clean, and covers the wet bulb completely with a snug fit.

CONCLUSION

The ultimate goal of calibration is to ensure accuracy of the unit under test. To ensurethat the accuracy is maintained with a high level of confidence, all potential sources oferror during the calibration must be analyzed. The best way to determine and evaluateerrors in relative humidity measurement is still by direct calculation, not via charts.With the increase of industry implementation of quality standards such as ISO 9000, thetime has come for metrologists to re-examine and re-evaluate measurement parametersthat were taken for granted up to this time. Whh the revolution of the personal computerand easy-to-use sofiware, accepting the inaccuracies of charts has become archaic. Newmathematicscomputation programs allow metrologists to evaluate with little difficultyphysical and mathematical concepts that were once a monumental task. During thisdiscussion one of the more challenging measurement calculations, the relation of relativehumidity using a psychrometer, was examined. A working model incorporating personalcomputers and software was employed as a tool to increase the both the accuracy ofmeasurement and the productivity of the metrologist.

Today’s metrologist has the advantage of an incredibly powerfhl tool---not a newmeasurement device---but none-the-less a tool that can enhance the accuracy offimdamental calculations. The psychrometer, an old technology, and the processes used todetermine relative humidity are made more expedient and accurate by the personalcomputer, a modern technology.


ACKNOWLEDGEMENTS

The Author would like to thank Bob Hardy of Thunder Scientific Corporation forproviding a technical review of this paper, and Bernard Morris of Automatic SystemsLaboratories Incorporated for providing additional reference papers. I would also like tothank my wife Kari Jo Bloomer for her many hours of editing work, and the managementstaff of GTE for providing me the time to complete this project.

REFERENCES

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BSWASHRAE STANDARD 41 .6-1982R“Standard Method for Measurement of Moist Air Properties”Revised Draft, May 1994

ISO/IEC/OIML/BIPM“Guide to the Expression of Uncertainty in Measurement”1992 (E)

John C. Kotz and Keith F. Purcell“Chemistry and Chemical Reactivity” 2nd EditionSaunders College Publishing1991

General Eastern Instruments“General Eastern’s Humidity Handbook”Revision B.00, May 1993

U.S. NavyNAVAIR 17-35QAL-2“Training Manual, Physical Measurements”Change 2-1, October 1982

Bernard Morris“A Reference Psychrometer and Read-Out System for Measurement of Wet andDry Temperatures, with ‘On Board’ Calculation of Relative Humidity and DewPoint”Automatic Systems Laboratories Inc.


1995 - an error analysis of … to “swing” a sling type psychrometer in a humidity chamber. in...

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