Conversion factors for SI units

A number of electrical terms evolved from the CGS system may still be encountered as well as units in the FPS system and other special units. In general it is best to convert units to the SI system before inserting quantities into equations as this will avoid problems involving conversion factors in the equations themselves. The engineering units which may be encountered in other systems of units are listed in Tables 22.4 to 22.6 with the conversion factor to give SI units.

D2

Dc

T

Where

= temperature rise t = time the current flows

T = time for speed change

J = inertia of rotating mass

N = speed change

M = torque applied

The units of J may be kg m2 which can be expressed as ML2. The units of n may be revolutions per second or radians per second for which revolutions and radians have no basic units giving the units of n as 1/s which translates to 1/T. The units of torque may be Nm where N can be replaced by the basic units kg m/s2 giving (ML/T2) L = ML2/T2 representing torque. A mis­take could be made at this stage if torque is given as kgf m and then the units are translated as ML. Substituting the correct M, L and T expressions into equation 22.1 gives:

 

Quantity

Unit

Conversion factor

SI unit

Cable

219.456

Chain (Gunter’s)

20.116 8

Chain (Ramden’s)

30.48

Fathom

1.828 8

Feet

0.304 8

Furlong

201.168

Inch

0.025 4

Length

M

Micron

1 x 10’b

Mile (nautical Brit)

1.853 184 x103

Mile (nautical Int)

1.852 x 103

Mile (statute)

1.609 34 x 103

Mil

2.54 x10’5

Rod

5.029 2

Yard

0.914 4

Acre

4.046 856 x103

Are

100

Area

M2

Centare

1

Hectare

1 x 104

Barrel (Brit)

0.163 65

Barrel (US petrol)

0.158 98

Barrel (US dry)

0.11563

Barrel (US liquid)

0.11924

Gallon (Brit) (Imp)

4.545 9 x 10 3

Gallon (US dry)

4.404 8 x10 3

Gallon (US liquid)

3.785 3x 10-3

Litre

1 x 10-3

Volume

Ounce (Brit fluid)

2.841 225 x 10"5

M3

Ounce (US fluid)

2.957 373x 1 O’5

Pint (Brit) (Imp)

5.682 4 x 10-4

Pint (US dry)

5.505 95 x 10-4

Pint (US liquid)

4.731 63 x 10"4

Quart (Brit) (Imp)

1.136 49 x 10-3

Quart (US dry)

1.101 19 x 10’3

Quart (US liquid)

9.463 2 x 10’4

 

ML 1/T

ML2 / T2

 

T

 

Equ 22.2

 

T

 

Which shows the units are consistent. If the error above had been made the unit of time would be given as L/T and this would have been a clear indication that something was amiss.

A more complicated example, involving both electrical current (A) and temperature (K) units, is the rate of temperature rise of a current carrying conductor assuming all the heat generated is stored within the conductor, which is given by:

 

Conversion factors for SI units

Equ 22.3

 

To obtain the quantity in SI units, the original units should be multiplied by the conversion factor, for example, to convert a length of 10 inch to metre units multiply by 0.025 4 giving 0.254 m. To convert from one non-SI unit to another non-SI unit, first convert to the SI unit by multiplying by the conversion factor and then convert to the other non-SI unit by dividing by the con­version factor for the other unit. If multiple units are involved, convert each separately by multiplying by the appropriate con­version factor for any units with positive powers and dividing by the appropriate conversion factors for any units with negative powers. For example, to convert lb/in3 (or lb in-3) to SI units mul­tiple by 0.453 6 to convert lb to kg and divide by 0.025 43 to con­vert in-3 to nr3 giving 27 680 kg rrv3 (or 27680kg/m3).

To convert Fahrenheit to Celsius or centigrade subtract 32 and then multiply by 5/9

To convert Fahrenheit to Rankine add 459.67

To convert Celsius and centigrade to Kelvin add 273.15

To convert Rankine to Kelvin multiply by 5/9

For temperature conversion to Kelvin (K) the following should be noted:

Absolute zero = 0 Kelvin

0 Rankine

-273.15 Celsius

-273.15 centigrade

-459.67 Fahrenheit

Ice point = 273.15 Kelvin

491.67 Rankine

0 Celsius

0 centigrade

32Fahrenheit

Quantity

Unit

.. ..

Conversion factor

SI unit

Energy

And

Work

British Thermal Unit (Btu) Btu (1ST)

Btu (mean)

Btu (39 F)

Btu (60 F) calorie, gm (cal, gm) cal, gm (mean) cal, gm (15 C) cal, gm (20 C) calorie, kg (cal, kg) cal, kg (mean) centigrade heat unit (15°C) erg

Foot-pound

1.54 35 x 103

1.55 04 x 103

1.55 87 x 103 1.059 66 x 103 1.054 68 x 103

4.184 4.19 4.186 4.182 4.184 x103 4.19 x103 1.898 3x 103 1 x 10’7 1.355 82

J

Force

Dyne

Kilogramme force poundal

1 x 10-5 9.807 0.138 255

N

Mass

Hundredweight (long) hundredweight (short) ounce (troy) ounce (avdp) pounds (troy) pounds (avdp) slugs ton (long) ton (short) ton (metric) (tonne)

50.802 3 45.359 2 0.031 103 0.028 35 0.373 241 0.453 592 14.593 9 1.106 046 x 103 9.071 847 x 102 1 x 103

Kg

Power

Cheval-vapeur horsepower horsepower (boiler) horsepower (metric)

735.499 746

9.809 5 x 103

735.499

W

Quantity

Unit

Conversion factor

SI unit

Atmosphere (atm) bar

Inch of mercury (32°F) (in Hg)

1.103 25 x 105 1 x 105 3.386 4 x 103

Pressure

Inch of mercury (60°F) (in Hg) inch of water (4°C) (in H20) mm of mercury (0°C) torr

3.376 1 x 103 0.248 7

133.313

133.313

Pa

Velocity

Knot

0.514 4

M/s

Viscosity

Centipoise (cp)

1 x 10-3

(dynamic)

Poise (p)

0.1

Viscosity

Centistoke (cSt)

1 x 10‘6

M2/s

(kinematic)

Stoke (St)

1 x 104

Table 22.5 Conversion factors for quantities related to mechanics

Quantity

Unit

Conversion factor

SI unit

Electric charge

Faraday (chem) Faraday (phys)

9.649 x 104 9.652 x 104

C

Magnetic flux

Line

Maxwell

1 x 10 s 1 x 10’8

Wb

Magnetic flux density

Gauss

1 x 10"

T

Magnetizing force

Oersted

79.577 47

A-turns/m

Magnetomotive force

Gilbert

0.795 77

A-turns

Table 22.6 Conversion factors for quantities

Detailed conversion information is now given for a number of different quantities.

Plane angle

Quantity designation:

SI unit: radian, rad.

Normal multiple units: mrad, rad.

Example: 2 rad = 2 x 57.2958 = 114.5916°

Rad

… g gon, grade

Degree

Minute

Second

Angular

Mil

63.6620

57.2958

3.43775 x 103

0.206265 x 106

1.00268 x 103

15.7080 — 10’3

0.9

54

3.24 x 103

15.75

17.4533 ■ 10’3

1.11111

60

3.6 x 103

17.5

0.290888 — 10’3

18.5185

— 10’3

16.6667 ■ 10‘3

60

0.291667

4.84814 ■ 10’6

0.308642 ■ 10’3

0.277778 • 10’3

16.6667

10’3

4.86111

10’3

0.997331

IO’3

63.4921 — 10’3

57.1429 ■ 10-3

3.42857

205.714

1

Grade (g) (or gon), 1 g = 1 gon = /200 rad.

1°= /180 rad.

For some purposes, the angular mil is taken to be 10’3 rad. The figures shown here are based on the concept that an angular mil is equal to 360/6400 degrees.

NOTE: 1 grade (… g) = 1 /100 of a right angle

Length

Quantity designation I. SI unit: metre (m).

Normal multiple units: km, cm, mm, . Example: 3 in = 3 * 25.4 * 10’3 = 76.2 x 10’3 m

Metre

M

Inch

In

Foot

Ft

Yard

Yd

Mile

39.370

3.2808

1.0936

0.62137 ■ 10’3

25.4 ■ 10‘3

1

83.333 IO’3

27.778 103

15.783 • 10 6

0.3048

12

1

0.33333

0.18939 103

0.9144

36

3

0.56818 10’3

1.6093 103

63.36 103

5.28 ■ 103

1.76 ■ 103

1

1.852 103

72.913 — 103

6.0761 ■ 103

2.0254 ■ 103

1.1508

1 nautical mile = 6080 ft = 1853.184 m 1 A, 1 Angstrom = 10_1° m 1 astronomic unit = 0.1496 • 1012 m 1 light year = 9.4605 • 1015 m 1 parsec = 30.857 • 1012 m

Area

Quantity designation: A.

SI unit: square metre (m2).

Normal multiple units: km2, dm2, cm2, mm2. Example: 4 ft2 = 4 -92.903 -10-3= 0.371612 m2

M2

In2

Ft2

Yd2

Acre

Square mile mile2

1

1.5500 — 103

10.764

1.1960

0.24710 — 10’3

0.38610 ■ 10’6

0.64516 — 10’3

1

6.9444 • 10’3

0.77161

• 10*3

0.15942 • 10’6

0.24910 ■ 10"9

92.903 ■ 10-3

144

1

0.11111

22.957 ■ 10’6

35-870 ■ 10’9

0.83613

1.296 — 103

9

1

0.20661 — io-3

0.32283 ■ 10’6

4.0469 ■ IO3

6.2726 ■ 106

43.56 ■ 103

4.84 — 103

1.5625 ■ IO3

2.5900 ■ 106

4.0145 ■ 109

27.878 ■ 106

3.0976 ■ 106

640

1

1 acre = 100 m2

1 hectare = 100 acres = 10000 m2

Volume

Quantity designation: V.

SI unit: cubic metre (m3).

Normal multiple units: dm3, cm3, mm3.

Non SI unit: litre (I): 1 I = 0.001 m3 = 1 dm3.

Normal multiple units: cl, ml.

Example:

5 US gallon = 5 • 3.7854 • 10 3 = 18.927 • 10’3 m3 = 18.927 I

M3

In3

Ft3

Yd3

UK gallon

US gallon

1

61.024 ■ 103

35.315

1.3080

219.97

264.17

16.387

• io-6

0.57870 • IO’3

21.434 • IO6

3.6046 ■ IO’3

4.3290 • IO’3

M3

In3

Ft3

Yd3

UK gallon

US gallon

28.317 ■ 10 3

1.728 ■ 103

1

37.037 ■ 10’3

6.2288

7.4805

0.76456

46.656 • 103

27

1

168.18

201.97

4.5461 • 10 3

277.42

0.16054

5.9461

■ io-3

1

1.2010

3.7854

• io-3

231

0.13368

4.9511 • IO’3

0.83268

1

Gross (register) tonnage used in shipping 1 ton = 100 ft3 = 2.83168 m3

1 UK fluid ounce, fl oz = 28.4131 cm3

1 US fluid ounce, fl oz = 29.5735 cm3

Time

Quantity designation: t.

SI unit: second (s).

Normal multiple units: ms, s, ns.

Non SI units: day (d), hour (h), minute (min). Example: 100000 s = 100000/3600 = 27.778 h

S

Min

H

D (day)

Week

16.6667 10 3

0.277778 ■ IO3

11.5741

■io-6

1.65344

10-6

60

1

16.6667 ■ IO3

0.694444

■ io-3

99.2063

10^

3.6 ■ 103

60

1

41.6667

■ io-3

5.95238

■ io-3

00

Oi

A

O

1.44 — 103

24

1

0.142857

604.8 ■ 103

10.08 • 103

168

7

1

1 tropical year = 31556925.974 s = 365.24219878 d 1 sidereal year = 31558150 s 1 calendar year = 365 d = 8760 h

Linear velocity

Quantity designation: v.

SI unit: metre per second (m/s).

Normal multiple units: km/h.

M/s

Km/h

Ft/s

Mite/h

1

3.6

3.2808

2.2369

0.27778

0.91134

0.62137

0.3048

1.0973

0.68182

0.44704

1.6093

1.4667

1

0.51444

1.852

1.6878

1.1508

1 knot = 1 nautical mile per hour = 1.853 km/h

Linear acceleration

Quantity designation: a.

SI unit: metre per second squared (m/s2).

M/s2

Cm/s2

Ft/s2

In/s2

G

100

3.2808

39.37

0.10197

10 x 10-3

1

32.808 — 10-3

393.7 10-3

1.0197 ■ IO 3

0.3048

30.48

12

31.081 IO’3

M/s2

Cm/s2

Ft/s2

In/s2

G

25.4 x 10-3

2.54

83.33 ■ 10-3

2.59 ■ 10 3

9.80665

980.665

32.174

386.09

1

Angular velocity

Quantity designation: .

SI unit: radian per second (rad/s).

The SI and Imperial units are identical.

Angular velocity is normally calculated from N revolutions/s by

2 N

Angular acceleration

Quantity designation: a.

SI unit: radian per second squared (rad/s2)

The SI and Imperial units are identical.

Mass

Quantity designation: m.

SI unit: kilogram (kg).

Normal multiple units: g, g, mg.

Non SI unit: tonne (t) = 1000 kg.

Kg

Lb (pound)

Oz (ounce)

Hundred* weight cwt (UK)

Ton (UK)

1

2.2046

35.274

19.684 ■ 10 3

0.98421 ■ 10-3

0.45359

16

8.9286 • 10-3

0.44643 ■ 10’3

14.594

32.174

514.79

0.28727 ■ 10-3

14.363 10-3

28.350 x 10 3

62.5 x 10 3

0.55804 ■ 10-3

27.902 10’6

50.802

112

1.792 — 103

1

50 ■ 10-3

O

5

P

2.24 ■ 103

35.84 — 10-3

20

1

Oz = ounce, also called ounce avoirdupois

1 ounce troy = 31.1035 ■ 10’3 kg

Cwt = hundredweight

USA cwt = 100 lb USA ton = 2000 lb

Also called specific weight.

Quantity designation: .

SI unit: kilogram per cubic metre (kg/m3) Non SI units: kg/dm3, g/cm3.

Kg/m3

G/cm3

Lb/in3

Lb/ft3

1

10 3

36.127 — 10-6

62.428 ■ 10-3

103

1

36.127 ■ 10’3

62.428

27.680 — 103

27.680

1

1.728 — 103

16.019

16.019 ■ 10"3

0.57870 ■ 10 3

1

The term specific gravity or relative density is also used and is the ratio of the mass of a given volume of substance to the mass of an equal volume of water at temperature of 4 °C and a pres­sure of 101 .325 kPa absolute. The density of water at 4 °C and 101.325 kPa absolute is 1000.02 kg/m3.

Quantity designation: F.

SI unit: newton (N).

Normal multiple units: MN, kN.

N

Dyn

Kiiogram-force, kgf kilopond,

Pound>force

Ibf

0.1 106

0.10197

0.22481

10 ■ 10-6

1.0197 • 10-6

2.2841 • 10’6

9.8066

0.98066 106

2.2046

4.4482

0.44482 ■ 106

0.45359

1

Torque

Quantity designation: T.

SI unit: Newton metre (Nm). Normal multiple units: MNm, kNm.

Nm

Kgf m

Ibf x in

Ibf x ft

0.10197

8.8508

0.73756

9.8066

86.796

7.2330

0.11299

11.521 ■ 10-3

83.333 ■ 10-3

1.3558

0.13826

12

1

Torque, power and speed are related by the formula: P = 2 NT

Pressure, stress

Quantity designation: p, , .

SI unit: Pascal (Pa), 1 Pa = 1 N/m2.

Normal multiple units: GPa, MPa, kPa and for stress: MN/m2, N/m2, N/mm2.

Pa

Bar

Kgf/cm2

Technical

Atmos

Kgf/mm2

Torr (= mm Hg)

Standard

Atm

Lbf/in2

(psi)

1

10 ■ 10’6

10.197 ■ 10’6

0.10197 ■ 106

7.5006 ■ 10’3

9.8692 — 10-6

0.14504 • 10-3

100 ■ 103

1.0197

10.197 ■ 10’3

750.06

0.98692

14.504

98.066 ■ 103

0.98066

Ф

O

735.56

0.96784

14.223

9.8066 ■ 106

98.066

100

73.556 ■ 103

96.784

1.4223 — 103

133.32

1.3332

10-3

1.3595 — 10-3

13.595 ■ 10-6

1

1.3158 — 10-3

19.337 ■ 10-3

101.32 ■ 103

1.0132

1.0332

10.332 ■ 10-3

760

1

14.696

6.8948

103

68.948 • IQ’3

70.307 ■ IQ’3

0.70307 • IQ’3

51.715

68.046 ■ 10’3

1

The preferred pressure unit for fan applications is the “bar”.

1 mm H20 9.81 Pa

1 in H20 249.09 Pa

1 in Hg 3386.4 Pa

1 Ata = 1 technical atmosphere (absolute)

1 Atu = 1 technical atmosphere (gauge)

Energy

подпись: energy

Dynamic viscosity

подпись: dynamic viscosity

Quantity designation: .

SI unit: Pascal second Pa s. Normal multiple units mPa s (= cP).

N s/m2

N s/mm2

P (poise)

CP m Pa s

1

10-6

10

103

106

O

O

!

109

0.1

O : O

100

10 3

10 9

O

O

1

Kinematic viscosity

Quantity designation: .

SI unit: square metres per second (m2/s).

Normal multiple units: mm2/s.

For conversion to other units of viscosity see nomogram below.

M2/s

Mm2/s cSt

St (Stoke)

1

106

10 — 103

10 6

1

10 • 103

0.1 • 10’3

100

1

Kinematic SI unit Seconds Seconds Seconds

Viscosity Engler Kinematicftediwxxji Redwood2Sayb°lt Seconds Seconds

Centlstokes degrees viscosity (standard) Universal Ford cup DIN cup

CSt (mm2/s) *E m2/sec m ssu no. 4 no. 4

Quantity designations: E, W, Q, L, U depending upon the type of energy.

SI unit: Joule (J).

Normal multiple units: TJ, GJ, MJ, kJ, mJ.

Since 1 J = 1 Nm = 1 Ws then Nm and Ws can also be used for all types of energy. The unit Joule should, however, be used for expressing all types of energy.

1 erg = 0.1 x 10’6 J.

J

Joule

KWh

Kilowatt

Hour

Kgf m kilogram­force metre

Kcal

Kilo-

Calorie

Ch h metric horse­power hour

Ft. Ibf (foot pound- force)

Btu

(British

Thermal

Unit)

1

0.27778 ■ 106

0.10197

0.23885 ■ IO’3

0.37767 — 10’6

0.73756

0.94782 10 3

3.6 106

0.36710

■ 106

859.85

1.3596

2.6552 — 106

3.4121

■ 103

9.8066

2.7241 ■ 10-6

2.3423

10’3

3.7037 • 10’6

7.2330

9.2949 • 10 3

4.1868 ■ 103

1.163 ■ 10-3

426.94

1

1.5812

■ io-3

3.0880 ■ 103

3.9683

2.6478 ■ 106

0.73550

0.27 106

632.42

1

1.9529 ■ 106

2.5096 — 103

1.3558

0.37662

— 10-6

0.13826

0.32383 ■ 10’3

0.51206 • IO’6

1

1.2851 ■ 10 3

1.0551 • 103

0.29307 ■ 10 3

107.59

0.25200

0.39847 ■ IO’3

778.17

1

Conversion factors for SI unitsPower

Quantity designation: P.

SI unit: Watt (W).

Normal multiple units: GW, MW, kW, mW, W.

W

Kgf m/s

Kcal/s

Kcal/h

Ch

Metric

Horse­

Power

Hp

Horse­

Power

Ft Ibf/s

Btu/h

1

0.10197

0.23885 ■ 10-3

0.85985

1.3596 ■ 10 3

1.3410

— 10‘3

0.73756

3.4121

9.8066

2.3423 — 10 3

8.4322

13.333 ■ IO’3

13.151 • 10-3

7.2330

33.462

4.1868 • 103

426.94

CO © CO

5.6925

5.6146

3.0880 • 103

14.286 • 103

1.163

0.11859

0.27778 ■ 10-3

1.5812 • IO’3

1.5596 ■ IO’3

0.85779

3.9683

735.50

75

0.17567

632.42

0.98632

542.48

2.5096 • 103

745.70

76.040

0.17811

641.19

1.0139

550

2.5444 • 103

1.3558

0.13826

0.32383 ■ IO’3

1.1658

1.8434 ■ IO’3

1.8182 — 10-3

4.6262

0.29307

29.885

• 10-3

69.999 ■ 10’6

0.25200

0.39847

■ 10-3

0.39302 — 10-3

0.21616

1

Flow

Quantity designation: qv.

The above factors apply for values above 60cSt

подпись: the above factors apply for values above 60cstSI unit: cubic metre per second (m3/s). Non-SI units: I/s, ml/s, m3/h.

I gallon/ min Igpm

US gallon/ min USgpm

Barrel/

Day

Bpd

M3/s

M3/h

I/s

L/min

1

1.2009

41.175

75.768 • 10-6

272.76 ■ IO’3

75.768 — 10’3

4.5461

0.83268

34.286

63.09 ■ 10-6

227.12 ■ 10-3

63.09 ■ IO’3

3.7854

24.286 ■ 10"3

29.167 — IO 3

1

1.84

■ io-6

6.6244 ■ IO3

1.84

■ IO3

110.41

■ IO’3

13.198 ■ 103

15.85 ■ 103

543.44 — 103

1

3600

1000

60000

3.6662

4.4029

150.95

277.78 ■ 106

277.78 — IO’3

16.667

13.198

15.85

543.44

1.0 ■ IO’3

3.6

60

219.97

■ 10~3

264.17

— 10-3

9.0573

16.667

IO’6

60 ■ 10-3

16.667 — IO’3

1

1 barrel = 42 US gallon

Temperature

Absolute temperature: Quantity designation: T. SI unit: Kelvin (K).

Temperature: Quantity designation: t. unit degree Celsius (Centigrade) (°C).

Kelvin***

Scale

Celsius

Scale

Rankine

Scale

Fahrenheit**

Scale

Physical

Relation­

Ship

Relative

Temperature

Value

0 К

-273.15 °С

0 °R

— 459.67 °F

Absolute

Zero

273.15 К

0 °С

491.67 °R

32 °F

Melting point of ice*

273.16 К

0.01 °С

491.688 °R

32.018 °F

Triple point of water*

373.15 К

100 °С

671.67 °R

212 °F

Boiling point of water*

Relative

Temperature

Intervals

(diffs)

1 К 0.55556 К

1 °С 0.55556 °С

1.8 °R 1 °R

1.8 °F 1 °F

* For defined conditions

** Value in °C = -1 (value in °F -32) = (value in K -273.15)

5

*** Value in K = — x (value in °R)

Posted in Fans Ventilation A Practical Guide


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