USEFUL EQUATIONS FOR THE ABIH EXAMINATIONS
This list of equations is offered as assistance in taking the ABIH examinations. No assurance is given that this list is
complete or that the use of this list will assure the successful completion of any examination. The variables used are
the same as found in the reference source for the equation. No attempt has been made to standardize variables.
[Metric (SI) equations are in brackets]
VENTILATION
๐ = ๐๐ด ๐1๐ด1 = ๐2๐ด2 ๐๐ = ๐๐ + ๐๐ ๐๐1 + ๐๐1 = ๐๐2 + ๐๐2 + โ ๐๐๐ ๐ ๐๐ 1โ2 ๐๐โ = โ0
20 logP
SPLP
(๐นโ + 1)VP๐
0
20 logP
SPLP
๐ = 4005โ๐๐
๐๐ [๐ = 1.29โ
๐๐
๐๐] ๐๐ =
0
20 logP
SPLP
๐
40050
20 logP
SPLP
2
๐๐ [๐๐ =0
20 logP
SPLP
๐
1.290
20 logP
SPLP
2
๐๐] โ๐๐๐ ๐๐๐ก๐๐ฆ ๐๐๐ ๐ = ๐นโ๐ฅ๐๐๐
๐ถ๐ = โ๐๐
|๐๐โ| ๐๐๐ =
0
20 logP
SPLP
๐1
๐30
20 logP
SPLP
๐๐1 +
0
20 logP
SPLP
๐2
๐30
20 logP
SPLP
๐๐2 ๐ = 4005(๐ถ๐)โ
|๐๐โ|
๐๐(๐ด) [๐ = 1.29(๐ถ๐)โ
|๐๐โ|
๐๐(๐ด)]
๐ = 4005๐ถ๐๐ดโ|๐๐โ| ๐๐๐๐๐ = ๐๐๐๐ค๐๐โ๐๐๐๐๐ฃ
๐๐๐๐๐ค๐๐ ๐โฒ =
๐
๐๐ ๐ก2 โ ๐ก1 = โ
๐๐
๐โฒ๐๐
0
20 logP
SPLP
๐ถ๐2
๐ถ๐10
20 logP
SPLP
๐๐(๐บ โ ๐โฒ๐ถ๐2)
(๐บ โ ๐โฒ๐ถ๐1)= โ
๐โฒ(๐ก2 โ ๐ก1)
๐๐ ๐ =
(403)(๐๐บ)(๐ธ๐ )(๐๐)(106)
(๐๐)(๐ถ๐) [๐ =
(24)(๐๐บ)(๐ธ๐ )(๐๐)(106)
(๐๐)(๐ถ๐)]
๐๐โ๐๐๐๐๐ =60๐
๐๐ ๐ถ๐2 =
๐บ0
20 logP
SPLP
1 โ ๐
โ(๐โฒโ๐ก
๐๐)
0
20 logP
SPLP
๐โฒ ๐ถ๐2 = ๐ถ๐1๐
โ(๐โฒโ๐ก
๐๐) ๐2 = ๐1
0
20 logP
SPLP
๐2
๐1
0
20 logP
SPLP
3
0
20 logP
SPLP
๐ ๐๐2
๐ ๐๐10
20 logP
SPLP
๐2 = ๐1
0
20 logP
SPLP
๐2
๐1
0
20 logP
SPLP
2
0
20 logP
SPLP
๐ ๐๐2
๐ ๐๐10
20 logP
SPLP
2
๐๐๐ 2 = ๐๐๐ 1
0
20 logP
SPLP
๐2
๐1
0
20 logP
SPLP
5
0
20 logP
SPLP
๐ ๐๐2
๐ ๐๐10
20 logP
SPLP
3
๐น๐๐ = ๐๐๐๐ข๐ก โ ๐๐๐๐ โ ๐๐๐๐ ๐น๐๐ = ๐๐๐๐ข๐ก โ ๐๐๐๐
NOISE
๐๐๐ฟ ๐๐ ๐ฟ๐ = 20 ๐๐๐0
20 logP
SPLP
๐
๐00
20 logP
SPLP
๐ฟ๐ผ = 10 ๐๐๐
0
20 logP
SPLP
๐ผ
๐ผ00
20 logP
SPLP
๐๐๐ฟ2 = ๐๐๐ฟ1 + 20 ๐๐๐
0
20 logP
SPLP
๐1
๐20
20 logP
SPLP
๐ฟ๐ค = 10 ๐๐๐
0
20 logP
SPLP
๐
๐00
20 logP
SPLP
๐0 = 10โ12๐ค๐๐ก๐ก๐ ๐ฟ๐๐ = 10 log 0
20 logP
SPLP
1
๐โ
0
20 logP
SPLP
10
๐ฟ๐10
๐
๐=1
๐ก๐
0
20 logP
SPLP
020 log
PSPL
P
๐ฟ๐๐ = 10 ๐๐๐
0
20 logP
SPLP
โ 10
๐ฟ๐๐10
๐
๐=1 0
20 logP
SPLP
๐๐ฟ = 10 log
0
20 logP
SPLP
1
๐0
20 logP
SPLP
๐ฟ๐ = ๐ฟ๐ค โ 20 log ๐ โ 0.5 + ๐ท๐ผ + ๐ถ๐น [๐ฟ๐ = ๐ฟ๐ค โ 20 log ๐ โ 11 + ๐ท๐ผ + ๐ถ๐น] ๐ท๐ผ = 10 log ๐
%๐ท = 1000
20 logP
SPLP
๐ถ1
๐1+
๐ถ2
๐2+. . . +
๐ถ๐
๐๐
0
20 logP
SPLP
๐๐ =
๐๐
2(๐ฟ๐ด๐โ๐ฟ๐/๐ธ๐ ) ๐๐๐ด๐๐ = 10 ๐๐๐
0
20 logP
SPLP
%๐ท
1000
20 logP
SPLP
+ 85๐๐ต๐ด
๐๐๐ด = 16.61 ๐๐๐0
20 logP
SPLP
%๐ท
1000
20 logP
SPLP
+ 90๐๐ต๐ด ๐ =
(๐)(๐ ๐๐)
60 ๐ =
๐
๐ ๐2 = 2๐1 ๐๐ = โ๐1๐2 ๐2 = โ2
3๐1
USEFUL EQUATIONS FOR THE ABIH EXAMINATIONS
This list of equations is offered as assistance in taking the ABIH examinations. No assurance is given that this list is
complete or that the use of this list will assure the successful completion of any examination. The variables used are
the same as found in the reference source for the equation. No attempt has been made to standardize variables.
[Metric (SI) equations are in brackets]
GENERAL SCIENCES, STATISTICS, STANDARDS
๐๐๐ =๐๐๐๐๐ก๐๐
๐๐๐๐๐ฅ106 ๐๐๐ =
๐๐ฃ
๐๐๐ก๐๐ฅ106 ๐๐๐ =
๐๐/๐3๐ฅ24.45
๐. ๐ค.
๐1๐1
๐๐ ๐1=
๐2๐2
๐๐ ๐2 ๐๐๐ =
๐๐๐2
(๐๐ โ ๐๐)
18๐
๐ ๐ =๐๐๐ฃ
๐ ๐๐๐
๐ผ๐
๐ผ= ๐๐๐ ๐๐ป = โ๐๐๐10[๐ป+] ๐พ๐ =
[๐ป+]๐ฅ[๐ดโ]
[๐ป๐ด] ๐พ๐ =
[๐ต๐ป+]๐ฅ[๐๐ปโ]
[๐ต]
๐๐ก๐๐ก๐๐ = ๐1๐1 + ๐2๐2+. . . +๐๐๐๐ ๐ฃ๐๐๐๐/โ๐๐ง๐๐๐ ๐๐๐ก๐๐ =๐ ๐๐ก. ๐๐๐๐๐๐๐ก๐๐๐ก๐๐๐
๐๐ฅ๐๐๐ ๐ข๐๐ ๐๐ข๐๐๐๐๐๐๐ ๐๐ฟ๐๐๐๐ฅ =
๐ถ1
๐๐ฟ๐1+
๐ถ2
๐๐ฟ๐2+. . . +
๐ถ๐
๐๐ฟ๐๐
๐๐ฟ๐๐๐๐ฅ =1
๐น1๐๐ฟ๐1
+๐น2
๐๐ฟ๐2+ โฏ +
๐น๐๐๐ฟ๐๐
๐ ๐น =8
โ๐ฅ
24 โ โ
16 ๐ ๐น =
40
โ๐ค๐ฅ
168 โ โ๐ค
128 ๐ถ๐๐ ๐ =
(๐ถ๐ โ ๐ถ๐)๐ด๐
1000๐ด๐๐๐
๐ถ๐๐ ๐ = ๐ธ๐ด๐
1000๐๐ ๐ธ๐๐๐๐๐ ๐๐๐๐ ๐๐ก๐ฆ =
๐๐๐
โ๐ต
๐๐
๐ด๐ ๐ =
0.61๐
๐sin๐ผ ๐๐ท = โ
โ(๐ฅ โ ๐ฅ๐)2
๐ โ 1 ๐บ๐ = โ(๐ฅ1)(๐ฅ2). . . (๐ฅ๐)
๐
๐บ๐ = 10โ(log๐ฅ)
๐ ๐บ๐๐ท =84.13% ๐ก๐๐๐ ๐ฃ๐๐๐ข๐
50% ๐ก๐๐๐ ๐ฃ๐๐๐ข๐ ๐บ๐๐ท =
50% ๐ก๐๐๐ ๐ฃ๐๐๐ข๐
15.87% ๐ก๐๐๐ ๐ฃ๐๐๐ข๐ ๐๐ด๐ธ = 1.645๐ถ๐๐ก๐๐ก๐๐ ๐ถ๐ =
๐๐ท
๐
๐ธ๐ = โ๐ธ12 + ๐ธ2
2+. . . +๐ธ๐2 ๐ก =
๐ฅ1 โ ๐ฅ2
๐๐ท๐๐๐๐๐๐โ1
๐1+
1๐2
๐๐ท๐๐๐๐๐๐ = โ(๐1 โ 1)๐๐ท1
2 + (๐2 โ 1)๐๐ท22
๐1 + ๐2 โ 2
๐ฟ๐ถ๐ฟ =๐ถ๐ด
๐๐ธ๐ฟโ
๐๐ด๐ธโ๐12๐ถ1
2 + ๐22๐ถ2
2+. . . +๐๐2๐ถ๐
2
๐๐ธ๐ฟ(๐1 + ๐2+. . . +๐๐) ๐ ๐๐ฟ = ๐ฟ๐ถ๐ฅ๐ป๐๐ฅ๐๐๐ฅ๐ท๐๐ฅ๐ด๐๐ฅ๐น๐๐ฅ๐ถ๐ ๐ฟ๐ผ =
๐ฟ
๐ ๐๐ฟ
90%๐ถ๐๐๐ ๐ผ๐๐ก๐๐๐ฃ๐๐ = ๐ ยฑ 1.645๐๐ท
โ๐ ๐๐๐ยญ๐ ๐๐๐๐ 95%๐๐ถ๐ฟ ๐๐ ๐๐๐๐ = ๐ + 1.645
๐๐ท
โ๐
HEAT STRESS
๐๐ต๐บ๐ = 0.7๐ก๐๐ค๐ + 0.2๐ก๐ + 0.1๐ก๐๐ ๐๐ต๐บ๐ = 0.7๐ก๐๐ค๐ + 0.3๐ก๐ โ๐ = (๐ โ ๐) ยฑ ๐ถ ยฑ ๐ โ ๐ธ
USEFUL EQUATIONS FOR THE ABIH EXAMINATIONS
This list of equations is offered as assistance in taking the ABIH examinations. No assurance is given that this list is
complete or that the use of this list will assure the successful completion of any examination. The variables used are
the same as found in the reference source for the equation. No attempt has been made to standardize variables.
RADIATION
๐ผ2 = ๐ผ1
0
20 logP
SPLP
๐1
๐20
20 logP
SPLP
2
๐ ๐๐ = (๐ ๐ด๐ท)(๐๐น) ๐ท =๐ค๐ด
๐2 ๐ด = ๐ด๐(0.5)
๐ก๐1
2โ ๐ด๐ =0.693
๐12โ
๐๐ ๐ด = ๐ด๐๐
โ0.693๐ก๐1
2โ
๐ผ = (12โ )
๐ด๐ผ0 ๐ผ = (1
10โ )๐ต
๐ผ0 ๐ผ2 =๐ผ1
2๐
๐ป๐๐ฟ
๐ผ2 =๐ผ1
10๐
๐๐๐ฟ
๐ = 3.32log0
20 logP
SPLP
๐ผ1
๐ผ20
20 logP
SPLP
(๐ป๐๐ฟ) ๐ผ = ๐ผ0๐ต๐โ๐ข๐ฅ
1
๐12๐๐๐โ
=1
๐12๐๐๐โ
+1
๐12๐๐๐โ
๐12๐๐๐โ
=(๐1
2๐๐๐โ ) (๐12๐๐๐โ )
๐12๐๐๐โ + ๐1
2๐๐๐โ
๐ =๐ธ2
3770 ๐ = 37.7๐ป2 ๐ =
4๐
๐ด
๐ =0
20 logP
SPLP
๐๐บ
4๐๐ธ๐ฟ0
20 logP
SPLP
12โ
๐๐๐ป๐ =1
โ 0
20 logP
SPLP
4ฮฆ
๐๐ธ๐ฟโ ๐2
0
20 logP
SPLP
12โ
๐๐๐ป๐ =๐0
๐0 0
20 logP
SPLP
4ฮฆ
๐๐ธ๐ฟ0
20 logP
SPLP
12โ
๐๐๐ป๐ =0
20 logP
SPLP
๐ฮฆ cosฮธ
๐๐ธ๐ฟ0
20 logP
SPLP
12โ
๐ท๐ =1
โ 0
20 logP
SPLP
4ฮฆ
๐๐๐ฟโ ๐2
0
20 logP
SPLP
12โ
๐ ๐๐๐ก๐๐๐ ๐๐ฃ๐ =0
20 logP
SPLP
โ ๐น๐๐2๐
๐=1
๐0
20 logP
SPLP
12โ
t =0.003๐ฝ/๐๐2
๐ธ๐๐๐ ๐ก =
๐ธ๐ฟ
๐๐ฟ๐ฅ0.1โ ๐. ๐ท. = log
๐ผ0
๐ผ
๐ท๐ฟ = โ๐2 + โ 2๐2 ๐บ = 10๐
10โ
CONSTANTS AND CONVERSIONS
ยฐF=9/5(ยฐC)+32 ยฐR=ยฐF+460 K=ยฐC+273.15 molar volume at 25ยฐC, 1 atm=24.45L 1ft3 =28.32L
1 ft3 =7.481 U.S. gal 1L=1.0566 qt 1 inch = 2.54 cm 1 lb=453.6 grams 1 gram=15.43 grains
1 atm=14.7 psi=760 mm Hg=29.92 in Hg=33.93 ft water=1013.25 mbar=101,325 pascals
1 Curie=3.7x1010
disint/sec (Becquerel)= 2.2x1012
dpm 1 Gray=100 Rad 1 Sievert=100 Rem
1 Tesla=10,000 Gauss 1 BTU=1054.8 joules=0.293 watt hr 1 cal=4.184 joules
speed of sound in air at 68ยฐF (20ยฐC)=1130 fps (344 m/s) speed of light=3x108 m/s
Planckโs constant=6.626x10-27
erg sec Avogadroโs number=6.024x1023
gas constant, R=8.314 J/mole K=0.082 L atm/mole K density of air=1.29 g/L at atm, 0ยฐC
g=981 cm/sec2 =32 ft/sec
2 Ac =385 mm
2 for 25 mm filter Af=0.00785 mm
2
TABLE 6-3. Summary of Hood Airflow Equations
From ACGIHยฎ, Industrial Ventilation: A Manual of Recommended Practice for Design, 29th Edition. Copyright 2016. Reprinted with permission.
From ACGIHยฎ, Industrial Ventilation: A Manual of Recommended Practice for Design, 29th Edition. Copyright 2016. Reprinted with permission.
From ACGIHยฎ, Industrial Ventilation: A Manual of Recommended Practice for Design, 29th Edition. Copyright 2016. Reprinted with permission.