The International System of Units (1) is used in this Handbook ... .fr

Manual of Symbols and Terminology for Physicochem- ... Frequency. Hz (hertz). THz, GHz, MHz, kHz. Mass kg (kilogram) Mg, g, mg, jag ... GW, MW, kW, mW, uW.
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U n i t s J. Brandrup Wiesbaden, FR Germany

A. B. C. D. E.

A.

Introduction International Units Si-Prefixes Conversion Factors Conversion Table for SI vs. English-American Units

1-13 1-13 1-14 1-14 1-17

INTRODUCTION

The International System of Units (1) is used in this Handbook as far as possible, since this system has become obligatory in many European countries and since it is supported by the National Bureau of Standards (2) and the American Society for Testing and Materials (3). Only

cursory information is given here for units needed in this Handbook. Detailed information may be found in the following References: 1. "Si-units and recommendations for the use of their multiples and of certain other units'', ISO 1000-1973. 2. "The International System of Units (SI)", Eds. C. H. Page, P. Vigoreux, Natl. Bur. Std. Spec. Publ., 1981, 330. 3. "Standard Metric Practice Guide", ASTM E-380-85. 4. Manual of Symbols and Terminology for Physicochemical Quantities and Units; Pergamon Press, Oxford 1979 (Pure Appl. Chem., 51, 1 (1979). 5. F. S. Conant, using the SI units, Polym. Eng. ScL, 17, 222 (1977) (further references).

B. INTERNATIONAL UNITS Selection of multiples of the Si-unit

Quantity

Si-unit

Length Area Volume Time Frequency Mass Density Force

m (metre) m2 m3 s (second) Hz (hertz) kg (kilogram) kg/m3 N (newton)

km, cm, mm, jum, nm km2, dm2, cm2, mm2 dm3, cm3, mm3 ks, ms, us, ns THz, GHz, MHz, kHz Mg, g, mg, jag mg/m3; kg/dm3; g/cm3 MN, kN, mN, uN

Pressure

Pa (pascal) or N/m2

GPa, MPa, kPa, mPa, uPa

Stress Viscosity (dynamic) Viscosity (kinematic) Surface tension Energy, work, heat

Pa or N/m2 Pas m2/s N/m J (joule)

Power Temperature Thermal conductivity Heat capacity Specific heat Entropy Amount of substance Electrical resistance Electrical conductivity

W (watt) K (kelvin), 0C W/mK J/K J/(kgK) J/K mol (mole) ft S (I/ft)

GPa; MPa or N/mm2; kPa mPas mm2/s mN/m TJ, GJ, MJ, kJ, mJ GW, MW, kW, mW, uW

Accepted units used with SI

Units accepted temporarily 1A = 10 ~10 m

Non SI units that should not be used 1 JJ. = 10 ~6 m

litre (1, L) (1 1= 1 dm3) d, h, min Iy= 10 ~9 kg

t t/m3; kg/1 1 bar = 105 Pa 1 atm = 101325 Pa

Electronvolt (eV) IeV«1.602 x 10" 19 J

1 dyn = 10 ~5 N; pond, kilopond 101325 1 Torr = Pa /OU = 133.32Pa poise; 1P = 0.1 Pas stokes; 1 St= 1 cm2/s dyn/cm lerg=10~ 7 J lcal = 4.1868J I0K=IK 0.86kcal/(mhgrd)

kJ/K kJ/(kgK) kJ/K Mole

1/13

C

SI-PREFIXES

Factor

Prefix

Symbol

Factor

Prefix

Symbol

10 18 10 15 10 12 10 9 10 6 10 3 10 2 10 l

exa peta tera giga mega kilo hecto deca

E P T G M k h da

10 ~l 10 ~2 10 ~3 10 " 6 10 ~9 10 " 1 2 10 ~15 10 ~18

deci centi milli micro nano pico femto atto

d c m \i n p f a

in

ft

yd

thou or mil

3.281 8.333 x 10~2 1 3 8.334 xlO~ 5

1.094 2.778 x 10~2 3.333XlO" 1 1 2.778 x 10" 5

3.937 x 104 1.0 x l O 3 1.2 x 104 3.6 x 104 1

D.

CONVERSION FACTORS

Length

m

Im in ft yd thou or mil

1 2.540 xlO~ 2 3.048XlO- 1 9.144X10" 1 2.540 xlO~ 5

Area

m2

Im2 sq. in sq. ft sq. yd ar

1 6.452 x 10 ~4 9.29OxIO" 2 8.361 x KT 1 1.0 x l O 2

Volume

m3

1 m3 1 (lit) cu. in cu. ft cu. yd gal (US) gal (UK)

Mass lkg lbm ton (metric) ton (UK) cwt (UK) ton (US) ounce grain Density lkg/m 3 Mg/m 3 =g/cm 3 lbm/cu. ft lbm/cu. in lbm/gal (UK) lbm/gal (US)

3.937XlO 1 1 12 36 1.0 x l O " 3 sq. in 1.55OxIO3 1 1.44OxIO2 1.296 x 103 1.55OxIO5 1 (lit)

1 10~3 1.639 x 10 ~5 2.832 x 10~2 7.646XlO" 1 3.785 x 10~3 4.546 xlO~ 3

sq. ft

103 1 1.639 x 10 ~2 2.832 x 101 7.645 x 102 3.785 4.546

kg

lbm

1 4.536 x 10" 1 1 x 103 1.016 x l O 3 5.080 x 101 9.072 x 102 2.835 x 10~2 6.480 x 10 " 5

2.205 1 2.205 x 103 2.24OxIO 3 1.120 x 102 2.0 x 103 6.250 x 10~2 1.429 x 10 ~8

kg/m3 1 1.OxIO3 1.602 x 101 2.768 x 104 9.978XlO 1 1.198 x 102

1.076XlO1 6.994 x 10 ~3 1 9 1.076 x 103

sq. yd

ar

1.196 7.716 x 10 ~4 1.111 x 10" 1 1 1.196 x l O 2

l.OxlO" 2 6.452 x 10 ~6 9.29OxIO" 4 8.361 x 10" 3 1

cu. in

cu. ft

cu. yd

gal (US)

gal (UK)

6.102 x 104 6.102 x 101 1 1.728 x 103 4.666 x 104 2.31OxIO2 2.774 x 102

3.531 x 10l 3.531 x 10~2 5.787 x 10 ~4 1 2JxIO1 1.337 xlO" 1 1.605 x 10 - 1

1.308 1.308 x 10~3 2.143 x 10~5 3.703 x 10" 2 1 4.951 x 10~3 5.946 x 10~3

2.642 x 102 2.642 x 10" 1 4.329 x 10 ~3 7.481 2.02OxIO2 1 1.201

2.20 x 102 2.20 x 10" 1 3.605 x 10~3 6.229 1.682 xlO 2 8.327 x 10"1 1

ton (UK) (long ton) 9.842xlO~ 4 4.464 x 10~4 9.842XlO" 1 1 5.0 x 10~2 8.929 x 10" 1 2.790 x 10~5 6.378 x 10 ~8

Mg/m3 = g/cm3 1.0 XlO" 3 1 1.602 x 10" 2 2.768 x 101 9.978 x 10~2 1.198 x 10" 1

cwt (UK) (long cwt)

ton (US) (short ton)

ounce

grain

1.968xlO~ 2 8.929 x 10~3 19.68 2.OxIO 1 1 1.786 x 101 5.580 x 10" 4 1.276 x 10 ~6

1.102xl0~ 3 5.0 x 10~4 1.102 1.120 5.600 x 10" 2 1 3.125 x 10~5 7.143 x 10 ~8

3.527XlO 1 1.6 x 101 3.527 x 104 3.584 x 104 1.792 x 103 3.2 x 104 1 2.286 x 10 " 3

1.543 x 104 7.0 x 103 1.543 x 107 1.568 x 107 7.840 x 105 1.4 x 107 4.375 x 102 1

lbm/cu.ft 6.243 XlO" 2 6.243XlO 1 1 1.728 x 103 6.229 7.480

lbm/cu.in

lbm/gal (UK)

lbm/gal (US)

3.613 x 10" 5 3.613xlO~ 2 5.789 x 10~4 1 3.605 x 10~3 4.329 x 10~3

1.002 x 10~2 1.002XlO1 1.605 x 10" 1 2.774 x 102 1 1.201

8.345 x 10" 3 8.345 1.337 x 10" 1 2.310 x 102 8.327XlO" 1 1

Force IN kp lbf dyn tonf (UK) tonf (US)

N (kg m/s2)

kgf, kp

lbf

dyn

tonf (UK) (long ton)

tonf (US) (short ton)

1 9.807 4.448 1.0 x IO"5 9.964 x 103 8.896 x 103

1.02OxIO-1 1 4.536 x 10~! 1.020 x 10~6 1.016 x 103 9.072 x 102

2.248 x HT 1 2.205 1 2.248 x 10~6 2.240 x 103 2.0 x 103

1.0 xlO 5 9.807 x 105 4.448 x 105 1 9.964 x 108 8.896 x 108

1.004 x 10~4 9.842 x 10~4 4.464 x 10~4 1.004 x 10~9 1 8.929 x 10"1

1.124 x 10" 4 1.102 x 10~3 5.0 x 10~4 1.124 x 10~9 1.120 1

Pressure lPa(=lN/m2) IkPa 1 MPa (=1 N/mm2 1 bar ( = 0.1 MPa) lp/cm 2 t lkp/m 2 t lat^lkp/cm2)+ 1 atm( = 760Torr)t lTorr(= 1/760atm)f Psi (lbf/sq. in) f

Pa

MPa (N/mm 2 )

kPa

1 103 106 105 9.8IxIO 1 9.81 9.8IxIO 4 1.01325 x 105 1.33 x 102 6.895 x 103

10~3 1 103 102 9.8IxIO" 2 9.8IxIO" 3 9.8IxIO 1 1.01325 xlO 2 1.33XlO"1 6.895

10- 6 10" 3 1 10"1 9.8IxIO" 5 9.8IxIO" 6 9.81 x 10~2 1.01325XlO"1 1.33 x 10" 4 6.895 x 10" 3

bar

p/cm 2

kp/m 2

at+

atm*

Torrt

Psi (lbf/sq. in)t

10" 5 10" 2 10 ! 1 9.81 x 10"4 9.8IxIO" 5 9.8IxIO" 1 1.013 1.33 x 10" 3 6.895 xlO" 2

1.02 x 10" 2 1.02x10' 1.02 xlO 4 1.02 xlO 3 1 10" ! 103 1.033 x 103 1.36 7.03IxIO" 5

1.02XlO-1 1.02 xlO 2 1.02 x 105 1.02 xlO 4 10] 1 104 1.033 x 104 1.36XlO1 7.03IxIO" 6

1.02 x 10~5 1.02 xlO" 2 1.02x10" 1.02 10" 3 10~4 1 1.033 1.36 x 10" 3 7.031 x 10~2

9.87 x 10" 6 9.87 x 10" 3 9.87 9.87 xlO" 1 9.68 x 10 " 4 9.68 x 10" 5 9.68 xlO" 1 1 1.32 x 10" 3 6.805 xlO" 2

7.50xl0~ 6 7.50 7.5OxIO3 7.5OxIO2 7.36x10"' 7.36 x 10"2 7.36 xlO 2 7.6OxIO2 1 5.17IxIO" 1

1.450xl0~ 4 1.45OxIO-1 1.45OxIO2 1.45OxIO1 1.422 x 10 ~2 1.422 x 10~3 1.422XlO1 1.47OxIO1 1.934 x 10"2 1

Non SI units.

Stress l P a ( = lN/m 2 ) lN/mm 2 (= IMPa) lkp/cm2 ( = 1 at)t lkp/mm 2 t Psi lbf/sq. in

Pa

N/mm2

kp/cm 2t

kp/mm2t

Psi (lbf/sq. in)1

1 106 9.8IxIO 4 9.8IxIO 6 6.895 x 103

10" 6 1 9.8IxIO- 2 9.81 6.895 x 10~3

1.02 XlO" 5 1.02XlO1 1 102 7.031 x 10~2

1.02 xlO" 7 1.02XlO-1 10~2 1 7.031 x 10~4

1.45OxIO-4 1.45OxIO2 1.422XlO1 1.422 xlO 3 1

Non SI units.

Viscosity (dynamic) lPas mPas cP kps/m2 kph/m2 lbm/(fts) lbm/(fth) lbf s/sq. ft

Viscosity (kinematic) Im2Zs mm2/s m2/h cSt sq. ft/s sq. ft/h

Pas (Ns/rcm2) (kg/(sm)) 1 1.0 x 10- 3 1.0 xlO" 3 9.807 3.530 x 104 1.488 4.134 x 10~4 4.788XlO 1

mPas (mNs/m2)

cP

1.0 xlO 3 1.0 xlO 3 1 1 1 1 9.807 x 103 9.807 x 103 3.530 x 107 3.530 x 107 1.488 x 103 1.488 x 103 1 4.134 x 10" 4.134 x 10" 1 4.788 x 104 4.788 x 104

m2/s 1 1.0 x 10" 6 2.778 x 10~4 1.0 x IO' 6 9.290 x 10~2 2.581 x 10" 5

mm2/s 1.0 xlO 6 1 2.778 x 102 1.0 9.290 x 104 2.581 x 10" 1

kps/m 2

kph/m2

lbm/(fts)

1.02OxIO-1 1.020 x 10" 4 1.02OxIO-4 1 3.60 x 103 1.518 x 10"1 4.215 x 10~5 4.882

2.833 x 10 ~5 2.833 x 10~8 2.833 xlO~ 8 2.778 x 10" 4 1 4.215 x 10" 5 1.171 x IO"8 1.356 x l O " 3

6.720 x KT 1 6.720 x 10~4 6.72OxIO- 4 6.590 2.372 x 104 1 2.778 x 10" 4 3.2HxIO 1

m2/h 3.6OxIO3 3.60 x 10" 3 1 3.60 x 10- 3 3.345 x 102 9.290 x 10~2

cSt 1.0 x 106 1.0 2.778 x 102 1 9.290 x 104 2.581 x IO1

lbm/(fth) 2.419 x 103 2.419 2.419 2.372 x 104 8.540 x 107 3.60 x 103 1 1.158 x 105

sq. ft/s 1.076 x 10l 1.076 x 10~5 2.990 x 10"3 1.076 x 10~5 1 2.778 x 10~4

lbf s/sq. ft 2.089XlO" 2 2.089 x 10~5 2.089 x 10~5 2.048XlO- 1 7.373 x 102 3.103 x 10~2 8.634 x 10" 6 1

sq. ft/h 3.875 x 104 3.875 x 10~2 1.076 x 101 3.875 x 10" 2 3.60 x IO3 1

N/m (kg/s2)

Surface tension lN/m mN/m kp/m dyn/cm

Energy IJ kWh kpm PSh lbfft erg HPh kcal BTU a

J(Nm) (kgm 2 /s 2 ) 1 3.6OxIO6 9.807 2.648 x 106 1.356 1.0 x 10" 7 2.685 x 106 4.187 xlO 3 1.055 x 103

dyn/cm

1.02OxIO-1 1.020 xlO~ 4 1 1.020 x 10 ~4

1.0 xlO 3 1.0 9.807 x 103 1

kgfm kpm

Psh

lbfft

erg

HPh

kcal

BTUa

1.02OxIO-1 3.67IxIO 5 1 2.70 x 105 1.363 x 10"1 1.020 x 10 " 8 2.737 x 105 4.269 X^ 102 1.076 x 102

3.777xlO~ 7 1.360 3.704 xlO~ 6 1 5.120 x 10"7 3.777 x 10~14 1.014 1.581 x 10" 3 3.985 x 10" 4

7.376X10" 1 2.655 x 106 7.233 1.953 x 106 1 7.375 x 10" 8 1.980 x 106 3.088 x 103 7.782 x 102

1.OxIO7 3.6OxIO13 9.807 x 107 2.648 x 1013 1.356 x 107 1 2.685 x 1013 4.187 xlO 1 0 1.055 x 1010

3.725xlO~ 7 1.341 3.653 x 10~6 9.863 x 10"1 5.051 x 10~7 3.725 x 10~14 1 1.560 xlO~ 3 3.930 x 10~4

2.388xlO~ 4 8.598 x 102 2.342 x 10~3 6.324 x 102 3.238 x 10~4 2.388 x IO' 11 6.412 x 102 1 2.520 x 10"1

9.478xlO~ 4 3.412 x 103 9.295 x 10~3 2.510 x 103 1.285 x 10~3 9.478 x 10"11 2.544 x 103 3.968 1

kWh 2.778xlO~ 7 1 2.724 xlO" 6 7.355 x 10"1 3.766 x 10~7 2.778 x 10"14 7.457 x 10"1 1.163 xlO~ 3 2.931 x 10" 4

kgf/m (kp/m)

1.0 xlO 3 1 9.807 x 103 1.0

1 1.0 xlO~ 3 9.807 1.0 x 10 ~3

British thennal unit.

J (Nm) (kgm 2 /s 2 )

Heat 1J kcal BTU CHU Wh a

mN/m

kca! 2.388 x 10" 4 1 2.520 x 10" 1 4.539XlO" 1 8.598XlO" 1

1 4.187 xlO 3 1.055 x 103 1.90OxIO3 3.6OxIO3

BTU

CHU°

9.478 x 10~A 3.968 1 1.80 3.412

5.262 x 10" 4 2.203 5.552 x 10" 1 1 1.894

Centigrade heat unit.

Power

W (J/s) (kgm 2 /s 3 )

kgf m/s kpm/s

1W kpm/s PS HP erg/s ft lbf/s kcal/h BTU/h

1 1.020 x IO"1 9.807 1 7.355 x IO2 7.5 x IO1 7.457 x IO2 7.604 x 10l 1.0 x 10" 7 1.020 x 10~8 1.356 1.383 x 10" 1 1.163 1.186 x 10"1 2.931 x 10" 1 2.988 x 10~2

PS HP (metr) 1.360 x 10" 3 1.333 x 10~2 1 1.014 1.360 x IO"10 1.843 x 10" 3 1.581 x 10" 3 3.985 x 10" 4

HP 1.341 x 1.315 x 9.863 x 1 1.341 x 1.818 x 1.560 x 3.930 x

erg/s 10~3 10" 2 10" 1 10" 10 10" 3 10" 3 10" 4

1.0 x 107 9.807 x 107 7.355 x 109 7.457 x IO9 1 x 10~8 1.356 x IO7 1.163 x IO7 2.931 x IO6

ft lbffs 7.376 x 10"1 7.233 5.425 x IO2 5.50 x IO2 7.375 1 8.578 x 10" 1 2.162 x 10" 1

kcal/h

BTU/h

8.598 x 10" 1 8.432 6.324 x 102 6.412 x IO2 8.598 x 10~8 1.166 1 2.520 x 10" 1

3.412 3.346XlO1 2.510 x IO3 2.544 x IO3 3.412 x 10" 7 4.626 3.968 1

Thermal conductivity

W/mK (kgm/(s3K))

kcal/(mh°C)

BTU/(fth°F)

BTU/(inh°F)

BTU in/ (sq.fth°F)

1 W/(mK) kcal/(mh°C) BTU/(fth°F) BTU/(inh°F) BTU in/(sq. fth°F)

1 1.163 1.731 2.077 x IO1 1.442 x 10" 1

8.598 x 10~! 1 1.488 1.786 x IO1 1.24 x 10" 1

5.778 x 10~J 6.72OxIO" 1 1 1.2 x IO1 8.333 x 10~2

4.815 x 10~2 5.6OxIO" 2 8.333 x 10" 2 1 6.944 x 10~3

6.933 8.064 1.2XlO1 1.44 x IO2 1

Specific heat, heat capacity

J/kgK (m2Z(S2K))

kJ/(kgK)

kcal/(kg°C)

BTU/(lbm°F)

1 J/(kgK) kJ/(kgK) kcal/(kg°C) BTU/(lbm°F) Wh/(kgK)

1 1.0 x IO3 4.187 xlO 3 4.187 x IO3 3.6OxIO3

1.0 x 10 ~3 1 4.187 4.187 3.60

2.389 x 10 " 4 2.389 x 10" 1 1 1.0 8.598XlO" 1

2.389 x 10 ~4 2.389 x 10"1 1.0 1 0.8598

E.

C O N V E R S I O N TABLE FOR SI vs. E N G L I S H - A M E R I C A N U N I T S

SI to English-American unit

English-American unit to SI

Length I m = 1.0936 yd = 3.28 ft = 39.37 in 1 mm = 0.03937 in

lyd = 3 ft = 0.9144m l f t = 12 in = 0.3048 m Im = 25.4 mm

lkg = 2.20461b

lib = 0.45359 kg

1 N = l(kgm)/s 2 = 2.248 x 10" 1 lbf

I M = 4.448 N

1 Pa = 1 N/m 2 = 1.450 x 1O-4 lbf/in2

1 lbf /in 2 = 1 psi = 6.89475 x 103 Pa

Mass, weight

Force

Pressure 4

= 6.89475 x 10 ~2 bar

= 2.953 x 10 ~ in Hg = 4.015 x 10~ 3 inH 2 O

HnHg = 3.38638 x 103Pa = 3.38638 x 10"2 bar

1 bar = 105 Pa = 1.450 x 10l lbf /in 2 = 2.953 x 101UiHg

ImH 2 O = 2.49089 x 102Pa

2

= 4.015 x 10 HiH 2 O

= 2.49089 x 10 " 3 bar

Tension, stress lN/mm 2 = 1.450 x 10 2 lbf/in 2

1 lbf/in2 = 6.89475 x 10 " 3 N/mm 2

Dynamic viscosity IPas = (Ns)/m 2 = 2.089 x 10~2 (lbf s)/ft2 1

= lkg/(ms) = 6.72x 10" lbf/(ft s)

1 (lbf s)/ft2 = 4.78802 x 101 Pas llb/(fts) = 1.488 Pa s

Kinematic viscosity I m 2 / s = 1.076 x 101 ft 2 /s

Ift 2 /s = 9.29x 10~ 2 m 2 /s

U = I W s = INm = 7.376 x 10"1 ftlbf

1 ft lbf = 1.35582 J

Energy, quantity of heat

1

IkJ = 9.478 x 10- BTU

IBTU= 1.05506 kJ

Power, heat flow rate I W = I Nm/s = 7.367 x 10 - 1 (ftlbf)/s 1

= 1 J/s = 4.425 x 10 (ftlbf)/min = 3.412 BTU/h

l(ftlbf)/s= 1.35582 W 1 (ftlbf)/min = 2.25969 x 10~2 W 1 BTU/h = 2.93072 x 10" 1 W

Specific heat capacity 1 J/(kg K) = 2.388 x 10~ 4 BTU/(lb/ 0 F) 3

5

1 J/(m K) = 1.491 x 10~ BTU/(ft

3 0

F)

IBTU/(Ib 0F) =4.1868 x 10 3 J/(kgK) IBTU/(ft 3 0F) =6.71 x 10 4 J/(m 3 K)

Thermal conductivity 1 W/(mK) = 6.933 (BTUin)/(ft 2 h °F) = 5.778 x 10~ 1 BTU/(fth°F) = 4.815 x 10 " 2 BTU/(inh 0F)

1 (BTUin)/(ft2h °F) = 1.442 x 10^1 W/(mK) lBTU/(fth°F) = 1.7307 W/(m K) 1 BTU/(in h °F) = 2.07689 x 101 W/(mK)

English-American unit to SI

SI to English-American unit Heat flux density

lBTU/(ft 2 h) = 3.1546 W/m 2

l W / m 2 = 3.17x 10- 1 BTU/(ft 2 h)

1BTU/(in2 h) =4.54263 x 10 2 W/m 2

= 2.201 x Kr 3 BTU/(in 2 h) Heat transfer coefficient lW/(m 2 K) = 1.761 x 10- 1 BTU/(ft 2 h°F)

1 BTU/(ft2 h °F) = 5.678 W/(m 2 K)

1 (m2 K)/W = 5.678 (ft2 h °F)/BTU

1 (ft2h °F)/BTU = 1.761 x 10- 1 (m 2 /K)/W

I K = I 0 C = 1.8 0 F

1 0F = 5.555 x 10" 1 K = 5.555 x 10" 1 0C

Thermal resistance

Temperature

Conversion: Tc= ^(rF-32)

r F = | r c + 32

7 K = ^ Tp+ 255.372

TF = I (TK- 255.372)

TQ - Temperature in Celsius ( 0 C); T? - Temperature in fahrenheit (0F); TK -

Temperature in kelvin (K).