PSy Formula

8/8/2019 PSy Formula

1/24

Report 1994:17 (English)

Equations and formulas for air and air

contaminants

A literature review

Lars Olander


2/24

ii

Foreword

This publication has been compiled because I have missed such a publication. Naturally

this means that the selection has been influenced by my views. However, in most cases I

have included a formula rather than exclude it. To make the number of pages limited

the explanations are as short as possible. The result is that this formula compilation cannot be used as a text book but only as a reference book or as a guideline to the literature

in one specific field.

For this, the third edition (in English) dr. techn. Y. Jin has done a lot of work to check

and complete formulas and literature references. I have not had the opportunity to make

the formulas available in a form direct usable for computers. To make calculations it is

necessary to transfer actual formula to a suitable program. To facilitate using and

searching in this compilation a diskette with all the formulas is included. The formulas

are there written in WordPerfect 5.1 (DOS/Windows).

This revised version has been transferred to Word (Microsoft Word 97), probably theEquation Editor must be installed to read the formulas. Since the equation editors in

Word and WordPerfect do not agree on how to treat different symbols, there could be

some difficulties with differentiating some symbols.


3/24

iii

Contents

Page nrIntroduction 1

Books of tables and reference books 3

Text books 4

1 Properties of air and water vapor 71.1 The Ideal-Gas Law 8

1.2 Beattie-Bridgeman equation of state 9

1.3 Specific heat capacity for ideal gases 9

1.4 Temperature variation of specific heat capacity, viscosity and diffusion

coefficient 9

1.5 Air properties (at 100 kPa) 11

1.6 Water properties (at 100 kPa) 12

1.7 van der Waal's equation of state for water vapor 12

1.8 Water vapor pressure between 275 and 647 K 13

1.9 Mixture of air and water vapor: Density and vapor pressure 13

1.10 Specific enthalpy of air 15

1.11 Calculation of humid air's properties 15

1.12 Psychrometer formula 161.13 Air pressure variation with height 16

1.14 Connections between sight lenght and contaminant concentration 17

2 Basic flow equations 182.1 Navier - Stokes' equation 18

2.2 Euler's equations for frictionless flow 19

2.3 Bernoulli's equation 19

2.4 Equation of continuity 20

2.5 Dimensionsless numbers 21

3 Flow generation 263.1 Theoretical total pressure change for fans 26

3.2 Flow variations for fans 27

3.3 Pressure variations for fans 27

3.4 Power dependence for fans 27

3.5 Efficiency for fans 27

3.6 Air flow rate through critical orifice 27

3.7 Temperature increase of air in fans and ducts 29

4 Equations for pipe flow 304.1 General equations 31


4/24

iv

4.2 Laminar flow (Re


5/24

v

7.3 Evaporation from liquid baths 71

7.4 Evaporation from water baths 71

7.5 Evaporation from water surfaces 72

7.6 Evaporation from surfaces 73

7.7 Evaporation from open vessels 747.8 Leakage from vessels and pipes under pressure 75

7.9 Heat generation from electrical motors to the surroundings 75

7.10 Fibre generation from new fibre filters 76

7.11 Ozon generation from electrostatic filters 76

7.12 Corrosion of ducts 77

7.13 Vaporization of additives from plastic folie (PVC) 77

7.14 Vaporization of F-11 from polyurethan plates 77

7.15 Grinding machines 77

7.16 Falling powders' dust generation 79

7.17 Air flow generated by falling powder 80

7.18 Dust generation from pressure vessels containing powder 80

7.19 Particle generation from gas shielded welding 81

7.20 Airborne droplets from release of liquids under pressure 81

7.21 Vaporization of oil spill 81

7.22 Vaporization of organic solvents from water surfaces 83

7.23 Evaporation of solvents 84

7.24 Evaporation of liquid spills 94

8 Heat and contaminants from man 958.1 Man's heat balance 96

8.2 Fanger's comfort equation 96

8.3 Perception of thermal climate 978.4 Perception of heat 98

8.5 Perception of draught 99

8.6 Particle generation from man 100

8.7 Contaminant generation from man 101

8.8 Heat losses at low temperatures 101

9 Contaminants 1029.1 Contaminants in rooms 103

9.2 Particle deposition on surfaces 103

9.3 Ozone in rooms 1049.4 Resuspension 104

9.5 Permeability of water vapor through color layers 104

9.6 Heights of welding plumes in stable conditions with temperature gradient 105

9.7 Life-times for water drops 106

9.8 Vaporization of drops in air 106

9.9 Diesel exhausts in mines 107

10 Contaminant concentrations - air flow rates in rooms 10810.1 Ideal steady-state, total mixing 110

10.2 Time dependent total mixing 110

10.3 Correction for non-ideal mixing 110


6/24

vi

10.4 Time dependent total mixing with incoming concentration 110

10.5 Ozone in room with copying machines 110

10.6 Concentration in rooms of Radon (222) 111

10.7 Concentration in rooms of Thoron (Rn 220) 111

10.8 Radon concentration in room 11210.9 Time dependent contaminant generation 112

10.10 Ideal mixing, separate recirculation system, separate local exhaust with outlet

outside the room and with capture efficiency 11310.11 Age of air 115

10.12 Tracer gas measurements 115

10.13 Ventilation efficiency, definition 116

10.14 Air exchange efficiency, definition 116

10.15 Transport efficiency for air cooling systems - ATF 116

11 Contaminant concentrations - air flow with recirculation 11711.1 Central recirculation, total mixing 11811.2 Central recirculation, total mixing, steady-state 118

11.3 Local recirculation (local exhaust), total mixing 118

11.4 Local recirculation, total mixing 119

11.5 Local recirculation, staedy-state, total mixing 119

11.6 Local recirculation, steady-state, total mixing 119

11.7 Local and central recirculation, steady-state 119

11.8 Central recirculation 120

11.9 Contaminant concentration in occupied zone and from room air cleaner at recirculation 120

11.10 2-zone model with local exhaust and with leakage and recirculation 121

11.11 Room air cleaner's effect on contaminant concentration 121

12 Leakage: Flow rates and concentrations 12212.1 Wind pressure for free flow 122

12.2 General infiltration equation 123

12.3 Theoretical natural draught 123

12.4 Flow rates from thermal differences 124

12.5 Air lock, steady-state concentration, total mixing 124

12.6 Contaminant concentration, recirculation and leakage, total mixing 125

12.7 Contaminant concentration, leakage, total mixing 127

13 Properties of mixtures 12913.1 General equation for density of mixtures 129

13.2 Density of vapor-air-mixture 130

13.3 Concentration conversion 130

13.4 Viscosity of mixtures 131

13.5 Viscosity of vapor-air at different temperatures 131

13.6 Ions on particles at steady-state 132

13.7 Ions in air 132

13.8 Energy from electrostatic discharges 133


7/24

vii

14 Convective flow rates and velocities 13414.1 Criteria for draught (Rydberg) 135

14.2 Cold draught from windows 135

14.3 Air velocities from cold draught 136

14.4 Heat exchange between room air and surfaces I 13714.5 Heat exchange between room air and surfaces II 138

14.6 Heat exchange between room air and vertical, plane surfaces 138

14.7 Heat transfer from different surfaces through bouyancy 138

14.8 Natural ventilation 140

14.9 Influence of wind velocity and temperature difference on natural ventilation 141

14.10 Air velocity in plume above point heat source 141

14.11 Air flow rate in plume above point heat source 141

14.12 Air flow rate in plumes above hot sources 142

14.13 Air flow rate at upper edge of vertical surface of hot body 142

14.14 Air flow rate into hood close above heat source 14314.15 Air flow rate into hood above heat source 144

14.16 Air flow rate above horizontal surface 144

15 Local exhausts 14515.1 Velocity distribution from a point sink 146

15.2 Centerline velocity for tube end (free hood), circular or rectangular with a

length-width ratio less than 5 146

15.3 Centerline velocity from a flanged circular hood 147

15.4 Centerline velocity from a slot (aspect ratio larger than 5) 147

15.5 Centerline velocity from a flanged slot 147

15.6 Capturing hood above bath 148

15.7 Capture efficiency 148

15.8 Capture efficiency for hood above emission source 148

15.9 Exhaust flow rate for contained process with heat generation 149

15.10 Push-pull-system for surface treatment 149

15.11 Push-pull-system 150

16 Air cleaning 15116.1 Filtration efficiency for fibrous filters 152

16.2 Filtration efficiency for electrostatic filters 154

16.3 Efficiency for cyclones 15516.4 Efficiency for venturi precipitators 157

16.5 Efficiency for wet scrubbers 158

16.6 Efficiency for settlement chambers 160

16.7 Pressure loss in fibrous filter 161

16.8 Costs for fibrous filters 163

16.9 Absorption of gases in moving drops 163

16.10 Adsorption of gases in materials 164

16.11 Cleaning from gases by condensation 164

16.12 Break-through for solvents in breathing masks 164

17 Outside dispersion 16617.1 Gaussian plume model 167


8/24

viii

17.2 Exhausts of hot gases from smoke stacks (Oak Ridge model) 168

17.3 Exhausts of cold gases from smoke stacks (Sutton's model) 168

17.4 Concentration from exhaust of cold gas from smoke stacks 168

17.5 Lowest exhaust height 169

17.6 Demands on dilution of exhausts from buildings 16917.7 Exhausts from roof or on lee-side 170

17.8 Concentrations from exhausts 171

17.9 Velocity and concentration distribution for bouyant plumes in homogenous

surroundings 171

17.10 Particle transport in convection plumes 172

17.11 Dispersion of traffic contaminants 174

17.12 Road tunnel ventilation 175

18 Summary 176


9/24

1

Introduction

The introduction has not been translated since it only dscribes the reason for the

compilation of these formulas. It also describes why certain areas are not covered in thisreport. Since the introduction is included in the Swedish version, anyone interested

could look there.

Books of tables and reference books

Arbeitsmappe Heizung, Lftung, Klimatechnik. Dsseldorf, VDI-Verlag 1968-1971.

ASHRAE Handbook1986-1989 (4 vol.). Fundametals, Equipment, HVAC Systems andApplications, Refrigeration (SI-edition) American Society of Heating, Refrigerating and Air-

Conditioning Engineer. New York1986-1989.

Charlesworth PS: Air exchange rate and airtightness measurement techniques - An application

guide. International Energy Agency, Air Infiltration and Ventilation Centre, Coventry, 1988.

Dittes W, Goettling O, Wolf H: Arbeitsplatzluftreinhaltung. Schriftenreihe der Bundesanstalt

fr Arbeitsschutz, Fb Nr 438, Dortmund 1985.

Industrial Ventilation. A manual of recommended practice. 21th edition. AmericanConference of Governmental Industrial Hygienists. 1992.

Liddament MW: Air infiltration and calculation techniques - An application guide.

International Energy Agency, Air Infiltration and Ventilation Centre, Coventry, 1986.

Lide DR (Ed.): CRC Handbook of Chemistry and Physics. 73th edition. 1993.

Perry RH, Green DW and Maloney JO (Eds): Perry's Chemical Engineer's Handbook. 6th

edition. McGraw Hill, New York1984.

Rietschel/Raiss: Heiz- und Klimatechnik. 15:e upplagan. Springer-Verlag, Berlin. ErsterBand: Grundlagen, Systeme, Ausfhrung. 1968. Zweiter Band: Verfahren und Unterlagen zurBerechnung. 1970.

Rohsenow WM and Hartnett JP (Ed.): Handbook of Heat Transfer, McGraw Hill, New York

1973.

Teasler R: Klimatdata fr Sverige. Statens rd fr byggnadsforskning. 1972.

VVS-handboken, Tabeller och diagram. Frlags AB VVS. Stockholm 1974.

Text books


10/24

2

Basic theory and measurements

Beckwiht TG, Marangoni RD, and Lienhard JH: Mechanical Measurements (5th edition),

Addison-Wesley, New York1993.

Bird RB, Steward WE and Lightfood EN: Transport Phenomena, Wiley & Sons, New York1960.

Doebelin EO: Measurement systems - Application and design. McGraw-Hill, New York,

1966.

Schlichting H: Boundary-Layer Therory (7th editon), McGraw Hill, New York1979.

Ventilation and contaminant control

Alden L, Kane JM: Design of Industrial Ventilation Systems. 5th edition. Industrial Press,New York1982.

Awbi HB: Ventilation of Buildings. Chapmann & Hall, London 1991.

Baturin VV: Fundamentals of Industrial Ventilation. Pergamon Press 1972.

British Occupational Hygiene Society, Working Group on Ventilation Design: Controlling

Airborne Contaminants in the Workplace. B.O.H.S. Technical Guide No 7, Science Reviews

Ltd, Leeds 1987.

Brown RC: Air filtration. Pergamon Press, Oxford 1993.

Davies CN: Air filtration. Academic Press, London 1973.

Burgess WA, Ellenbecker MJ, Treitman RD: Ventilation for control of the work environment.

John Wiley & Sons, New York1989.

Dorman RG: Dust Control and Air Cleaning. Pergamon Press, Oxford 1974.

Goodfellow HD: Advanced Design of Ventilation Systems for Contaminant Control.

Chemical Engineering Monographs Vol. 23. Elsevier, Amsterdam 1985.

Goodfellow, H.D. (Ed.): Ventilation '85. Proceedings of the 1st International Symposium onVentilation for Contaminant Control, October1-3 1985, Toronto, Canada. Elsevier,Amsterdam 1986

Heinsohn RJ: Industrial Ventilation. John Wiley & Sons, New York1991.

Hemeon WCL: Plant and process ventilation. The Industrial Press, New York1963.

Hughes, R.T., Goodfellow, H.D., Rajhans, G.S. (Eds): Ventilation '91. Proceedings of the 3rd

International Symposium on Ventilation for Contaminant Control, September16-20, 1991,


11/24

3

Cincinnati, Ohio, USA. American Conference of Governmental Industrial Hygienists,

Cincinnati, Ohio USA 1993.

Jansson, A., Olander, L. (Eds): Ventilation '94. Proceedings of the 4th International

Symposium on Ventilation for Contaminant Control, held in Stockholm, September 5-9,

1994. Arbete och Hlsa 1994:18 (2 vols). National Institute of Occupational Health, Solna,

Sweden 1994.

Licht W: Air Pollution Control Engineering. 2nd Ed. Marcel Dekker, New York1988.

McDermott HJ: Handbook of Ventilation for Contaminant Control. Ann Arbor Science 1976.

McQuiston FC and Parker JD: Heating, Ventilating and Air Conditioning - Analysis and

Design (3rd edition), John Wiley & Sons, News York1988.

Mrmann H: Lufttechnische Anlagen fr gewerbliche Betriebe. Carl Marhold, Berlin 1980.

Olander L: Ventilation. Studentlitteratur1982.

Vincent, J.H. (Ed.): Ventilation '88. Proceedings of the 2d International Symposium on

Ventilation for Contaminant Control, 20-23 September1988, London, England, UK.Pergamon Press, Oxford 1989

Aerosols

A bibliography of Aerosol Science and Technology. Aerosol Science and Technology, vol.14,sid 1-4, 1991.

Aerosol Measurement Workshop: Aerosol Measurement. Eds. Lundgren, Harris, Marlow,

Lippmann, Clark, Durham. University Presses of Florida 1979.

Calvert S, Englund HM (Eds): Handbook of Air Pollution Technology, John Wiley & Son,

New York1984.

Committee on Medical and Biologic Effects of Environmental Pollutants, Subcommittee on

Airborne Particles: Airborne Particles. University Park Press, Baltimore 1979.

Friedlander SK: Smoke, Dust and Haze Fundamentals of Aerosol Behavior. Wiley-Interscience, New York1977.

Fuchs NA: The Mechanics of Aerosols. Pergamon Press 1964. (Reprint Dover1989)

Heskett HE: Fine Particles in Gaseous Media. 2nd Ed. Lewis Publishers, Michigan 1986

Hinds WC: Aerosol Technology. Properties, Behavior, and Measurement of Airborne

Particles. Wiley-Interscience, New York1982.

Israel G: Aerosols. Formation and Recetivity. Proceedings Second International Aerosol

Conference, September1986. Pergamon Press, Oxford 1986.


12/24

4

Liu BYH (Ed.): Fine particles. Aerosol Generation, Measurement, Sampling and Analysis.

Academic Press, New York1976.

Liu BYH, Pui DYH, Fissan HJ (Eds): Aerosols. Science, Technology and Industrial

Applications of Airborne Particles. First International Conference, Elsevier1984.

Marple VA, Liu BYH (Eds): Aerosols in the Mining and Industrial Work Environments. 3

Vol. Ann Arbor Science 1983.

Reist PC: Introduction to Aerosol Science. MacMillan 1984.

Shaw DT (Ed.): Fundamentals of Aerosol Science. Wiley-Interscience, New York1978.

Shaw DT (Ed.): Recent Developments in Aerosol Science. Wiley-Interscience, New York

1978.

Willeke K, Baron PA (Eds): Aerosol Measurement. Van Nostrand Reinhold, New York1993.


13/24

5

1 Properties of air and water vapor

This chapter includes some properties dependence of pressure, temperature, humidity etc and

data for the most important properties for air and water vapor. First is the ideal-gas law (1),which is usable for air at normal temperatures. For extreme pressures or temperatures an

equation of state (2) can be used. For ideal gases there exist a number of connections (3),which can be used for air. Some properties variation with temperature are presented in 4. In 5

are given figures for air and in 6 for water and water vapor. For water vapor can the ideal-gas

law be used for approximative calculations (1). If more accurate values are needed an equationof state is used (7,8). Mixtures of air and water vapor are frequent and formulas are presented

in 9. In 11 and 12 are formulas to be used when measuring water vapor in air. In 10 are someformulas for the variation of heat content with temperature and humidity. Air pressure

variation with height are given in 13. Some equations for connection between contaminantconcentration and sight length end this chapter (14).

If the pressure is not given or if it is not a part of the formulas, normal pressure i.e. 1.013 bar

(=101.3 kPa) is presumed.


14/24

6

1.1 The Ideal-Gas Law

TRM

m=VporTRn=VporTR=vp

p = pressure

v = molecular volume

R = gas constant (8,31441 J/mol,K = 1,9872 cal/K,mol =0,08205 lit,atm/K,mol = 62,4 lit,mm Hg/K,mol)

T = absolute temperature

V = volume

n = number of mols

m = mass

M = molecular weight.

(Normally used for air, also when some water vapor or contaminants are present.)

1.2 Beattie-Bridgeman equation of state(Air from - 145 C to + 200 C)

p = pressure, atm

v = molecular volume, lit/mol

R = gas constant 0,08205 litatm/molKT = temperature, K.

(To be used at extreme pressures or temperaturs, or when more accurate values than

from (1) are needed).

1.3 Specific heat capacities for ideal gases

Cp = specific heat capacity at constant pressure

Cv = specific heat capacity at constant volume

a = air velocity

v

0,0193111,3012

Tv

104,341

v

0,01101+10,04611+vTR=vp

3

42

R+C=C vp

TR=/p=a


15/24

7

= isentrop exponent = Cp/Cv = densityR, T, p see 1.2.

1.4 Temperature variation of specific heat capacity, viscosity (see also13.4) and diffusion coefficient

a)

Cp in cal/mol,K in the temperature interval 300-1500 K.

b)

= viscosity in the interval 273-673 K, N,s/m2

T = temperature, K.

c) Another expression is

= viscosity, kg/m,sT = temperature, K.

d)

= viskosity at temperature T0 = viskosity at temperature T0.

e) In small intervals this can be simplified to

T100,2656T101,762+6,386=C263

p

T

123,6+1

T10150,3=

8

110+T

T101.45=

2/36

110+T

110+T)

T

T(= 0

0

2

3

0


16/24

8

where 0.5 < < 1 depends on interval.

f)

D(H2O in air) = diffusion coefficient for water vapor in air, m2/h

p = total pressure, kPa/m2

T0 = 273 K.

g) For p = 760 mm Hg this will be

h) Another empirical formula for water vapor in air up to 1350 K is

D = diffusion coefficient for water vapor in air, mm2/s

p = pressure, kPa

T = temperature, K.

)T

T(=

00

)T

T(

p

805=air)inOH(D

0

1.80

2

/s)cm()273

T(0.216=D 2

1.80

)245+T

T()p

0.926(=D

2.5


17/24

9

1.5 Air properties (at 100 kPa)

Molecular weight M = 28.962458 g/mol

Density at 0C (dry air) = 1.2929 kg/m3

at 15C, 0% R.H, 105 Pa 1.2094 kg/m3

at 15C, 50% R.H, 105 Pa 1.2055 kg/m3

at 15C, 100% R.H, 105 Pa 1.2017 kg/m3

at 20C, 0% R.H, 105 Pa 1.1887 kg/m3

at 20C, 50% R.H, 105 Pa 1.1834 kg/m3

at 20C, 100% R.H, 105 Pa 1.1783 kg/m3

Heat conductivity at 18C = 0.025 W/mCSpecific heat capacity at 0C Cp = 1.00 kJ/kg,C

Cp = 29.0 kJ/kmol,K

Viscosity at 0C = 17.0 10-6 kg/s,mViscosity at 20C = 18.192 10-6 kg/s,mCritical temperature Tc = 132.5 KCritical pressure Pc = 36 bar

Melting point Ts = 60.1 KBoiling point Tk= 80.2 K

Density at boiling point = 880 kg/m3

Components of dry atmospheric air

N2 78.084 vol %

O2 20.946 "

Ar 0.934 "

CO2 0.033 " (variabel)Ne 18.18 ppmHe 5.24 "

Kr 1.14 "H2 0.5 "

Xe 0.087 "

CH4 2 "

N2O 0.5 "

O3 0.01 " (variabel)Rn 6 10-14 " (variabel)

Mean free path

l = mean free path of air molecules, m (15-25C, 0-100% RH) = air viscosity, kg/m,s = air density, kg /m3

P = air pressure, Pa

P8

I=l


18/24

10

I = constant = 0.4987445.

1.6 Water properties (at 100 kPa)

Molecular weight M = 18.0152 g/molDensity at 0C = 999.84 kg/m3

at 20C = 998.205 kg/m3

Heat conductivity at 20C = 0.598 W/m,CSpecific heat capacity at 0C Cp = 4.218 kJ/kg,K

at 20-100C Cp = 4.18 kJ/kg,KViscosity at 0C = 179210-6 kg/s,m

at 20C = 100210-6 kg/s,mMelting point ts = + 0C

Melting heat Qs = 334 kJ/kg

Boiling point tk= + 100CVaporization enthalpy Qk= 2257 kJ/kg

Density at boiling point (1.013 bar) = 958.35 kg/m3

Critical temperature Tc = 647.4 KCritical pressure Pc = 221.3 bar

Diffusion coefficient for water vapor in air

at 0C D = 0.216 cm2/sat 20C D = 0.245 cm

2/s

Schmidt number for water vapor in air

Lewis number for water vapor in air

1.7 van der Waal's equation of state (water vapor)

p in atmospheres

v in cm3/mol

C)(200.617

C)(00.616{=D=Sc

C)20(00.866=Pr

Sc=Le

TR=30.42)(v)v

105.454+(p

2

6


19/24

11

T in K

R = 82.054 atm,cm3/mol,K.

1.8 Water vapor pressure between 275 and 647 K

x =3.647

T1

T = temperature, K

pvp = vapor pressure, bar.

1.9 Mixture of air and water vapor: Density and vapor pressurea)

This can also be written in the following way:

= density for humid air, kg/m3

t = density for dry air, kg/m3

P = total pressure, mm Hg

Pv = partial pressure of water vapor, mm HgT = absolute temperature, K.

b)

pv = partial pressure for water vapor, in mbar, with water content x

(kg H2O / kg dry air)

x1

x1.23303x2.77580x1.45838x+7.76451=

221.2

pln

631.5vp

)T

p(0.176)

T

P v(0.465=

760

p0.3783P

T

273.13= v

t

1013

18

x+

29

118

x

=pv


20/24

12

(If1013 is changed to 760 the partial pressure is expressed in mm Hg.)

c)

, t and x see above.

(0.622 is MH2O/Mair= 0.62198)x, pv, P see above

d)

x = water content, kg/m3

td = dew point, C.

The partial pressure of water vapor for a specific dew point can be calculated by using

dew point temperature instead of air temperature in e orf.

e) Dry temperature above 0 C

f) Dry temperature below or equal to 0 C

pm = saturation pressure for water vapor, in mbar, at absolute temperature T.

x)+(1=t

pP

p622.0=x

v

v

10104.8=x 38t

3 d

0.78613974+110100.42873+

+101101.50474+

273.16

Tlog5.02808

T

273.16110.79586=)p(log

T

273.1614.769663

1273.16

T8.296924

m

786139740.+16.273

T18768170.+

T

16.273log566543.

T

16.2730969369.=)p(log m


21/24

13

g)

h)

pm = saturation pressure for water vapor, kPa

t = air temperature, C.

i) Air humidity variation with barometric pressure

= ptr/ ps equal to relative humidityptr = vapor pressure in air with temperature ttrps = saturation vapor pressure at temperature ttr , mm Hg

pf = vapor pressure in air at temperature tf , mm Hg

tf

= wet temperature, C

ttr = temperature (dry thermometer for air), C

b = barometric pressure, mm Hg

t = ttr- tf1510 = 755/k, where 755 = initial barometric pressure, mm Hgk = 0.5 mm Hg/K for water-air

= 0.4 mm Hg/K for ice-air.

1.10 Specific enthalpy of aira)

h = specific enthalpy, kJ/kg

t = temperature, C

Cp = specific heat capacity for dry air1.0 kJ/kg,CCp (H2O) = specific heat capacity for water vapor1.9 (1.8516) kJ/kg,Cx = water content kg H2O/kg dry air

r = specific vaporization enthalpy for water at 0C = 2500 kJ/kg.

C)26(0e0.62796=pt106.5557

m

2

C)50(26e83721.0=pt1041695.

m

2

p

1510)t /(bp

s

f

=

rx+O)H(Cxt+Ct=h 2pp


22/24

14

b)

1.11 Calculation of humid air's properties

By using dry temperature (tt), wet temperature (tv) and barometric pressure (P) it is

possible to calculate relative humidity (_), absolute humidity (x) and specific enthalpy

(i):

1 Calculate saturation pressure for water vapor (pm) by using 1.9.e.

2 Calculate absolute humidity for saturated state (xm with 1.9.c). (Put p= pm and xm isthe result.)

3 Absolute humidity (x) is calculated from

or from

(tt , tv in C, x and xm in kg/kg).

4 Relative humidity is calculated in % from = x/xm*100

5 Specific enthalpy is calculated from equation 1.10.b.

Dew point, partial pressure and density is calculated by using equations 1.9.d and1.9.b.

If the starting point is relative humidity instead of the wet temperature the following

calculations are done:

1 Calculate the saturation pressure for water vapor (pm) with 1.9.e.

2 Calculate partial pressure for water vapor (pv) from

xt)1.9+(2500+t=h

C0>tfor2500t86.1t19.4

2500)t27.(2x+)tt(1.005=x x

tv

vmtv

C0tfor2833t86.1t11.2

2833)t25.(0x+)tt(005,1=x t

tv

vmvt


23/24

15

3 Calculate absolute humidity for the saturated state (xm) with 1.9.c.

3 Calculate absolute humidity (x) from

5 Specific enthalpy is calculated from equation1.10.

1.12 Psychrometer formulaa)

pv = partial pressure for water vapor

pm = saturation pressure for water vapor

P = total pressure (pv, pm and P in the same units)

tt = dry temperature Ctv = wet temperature C

A = psychrometer constant

Thermodynamical constant A = 6.53*10-4/CAssmann psychrometer A = 6.62*10-4/CAir velocities larger than 5.5 m/sA = 6.5*10-4/CAir velocity 0 m/s A = 12*10-4/C

Natural ventilated thermometer A = 7.9* 10-4/C

For p = 101.3 103 Pa the Assmann psychrometer will give

Pv = pm - 67.1 (tt - tv) [Pa]

1.13 Air pressure variation with height

100

p=p mv

p

xp=x

m

mv

)tt(APp=p vtmv

m)1524(0e86425.101=ph1024087.1 4

m)3048(1525e12563.102=ph1025184.1 4


24/24

PSy Formula

Documents

Transcript of PSy Formula