# 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:

 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 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

-459.67 Fahrenheit

Ice point = 273.15 Kelvin

491.67 Rankine

0 Celsius

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:

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.

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: .

The SI and Imperial units are identical.

Angular velocity is normally calculated from N revolutions/s by

2 N

Angular acceleration

Quantity designation: a.

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

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

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

SI 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