2.4 Units and Conversions

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Units are essential when describing real things.

Good engineering practice demands that each number should always be accompanied with a unit.

2.4.1 How to Use Units

This section does not give an exhaustive list of conversion factors, but instead a minimal (but fairly complete) set is given. From the values below most conversion values can be derived.

A simple example of unit conversion is given below,

2.4.2 SI Units

1. Beware upper/lower case letter in many cases they can change meanings.

e.g. m = milli or mega?

2. Try to move prefixes out of the denominator of the units.

e.g., N/cm or KN/m

3. Use a slash or exponents.

e.g., (kgm/s2) or (kgms-2) or (kg m s**-2) or (kg m s ^-2)

4. Use a dot in compound units when possible.

e.g., Nm

5. Use spaces to divide digits when there are more than 5 figures, commas are avoided because their use is equivalent to decimal points in many places (e.g., Europe).

Base and derived units

In some cases units are non-standard. There are two major variations US units are marked with `US' and Imperial units (aka English and inch based) are marked with `IMP'.

2.4.3 A Table

Distance

1 ft. (feet) = 12 in. (inches) = 0.3048 m (meter)

1 mile = 1760 yards = 5280 ft = 1.609km

1 in.(inch) = 2.540 cm

1 yd (yard) = 3 ft.

1 nautical mile = 6080 ft. = 1852 m = 1.150782 mi

1 micron = 10-6 m

1 angstrom = 10-10 m

1 mil = 10-3 in

1 acre = 43,560 ft. = 0.4047 hectares

1 furlong = 660 ft

1 lightyear = 9.460528e15 m

1 parsec = 3.085678e16 m

Area

1 acre = 43,559.66 ft2

1 Hectare (ha) = 10,000 m2

1 Hectare (ha) = 10,000 m2

1 Hectare (ha) = 10,000 m2

1 Hectare (ha) = 10,000 m2

Velocity

1 mph = 0.8689762 knot

Angle

1 rev = 2PI radians = 360 degrees = 400 gradians

1 degree = 60 minutes

1 minute = 60 seconds

Volume

1 US gallon = 231 in3

1 CC = 1 cm3

1 IMP gallon = 277.274 in3

1 barrel = 31 IMP gal. = 31.5 US gal.

1 US gal. = 3.785 l = 4 quarts = 8 pints = 16 cups

1 liter (l) = 0.001 m3 = 2.1 pints (pt) = 1.06 quarts (qt) = 0.26 gallons (gal)

1 qt (quart) = 0.9464 l

1 cup (c) = 0.2365882 l = 8 USoz

1 US oz = 8 US drams = 456.0129 drops = 480 US minim = 1.0408 IMP oz

= 2 tablespoons = 6 teaspoons

1 IMP gal. = 1.201 U.S. gal.

1 US pint = 16 US oz

1 IMP pint = 20 IMP oz

1tablespoon = 0.5 oz.

1 bushel = 32 quarts

1 peck = 8 quarts

Force/Mass

1 N (newton) = 1 kgm/s2 = 100,000 dyne

1 dyne = 2.248*10-6 lb. (pound)

1 kg = 9.81 N (on earth surface) = 2.2046 lb

1lbf = 16 oz. (ounce) = 4.448N

1 oz. = 28.35 g (gram) = 0.2780N

1 lb = 0.03108 slug

1 kip = 1000 lb.

1 slug = 14.59 kg

1 imperial ton = 2000 lb = 907.2 kg

1 metric tonne = 1000 kg

1 troy oz = 480 grain (gr)

1 g = 5 carat

1 pennyweight = 24 grain

1 stone = 14 lb

1 long ton = 2240 lb

1 short ton = 2000 lb

Pressure

1 Pascal (Pa) = 1 N/m2 = 6.895 kPa

1 atm (metric atmos.) =760 mmHg at 0°C=14.223 lb/in2=1.0132*105 N/m2

1 psi = 2.0355 in. Hg at 32F = 2.0416 in. Hg at 62F

1 microbar = 0.1 N/m2

Scale/Magnitude

atto (a) = 10-18

femto (f) = 10-15

pico (p) = 10-12

nano (n) = 10-9

micro (m) = 10-6

milli (m) = 10-3

centi (c) 10-2

deci (d) = 10-1

deka (da) = 10

hecto (h) = 102

kilo (K) = 103

mega (M) = 106

giga (G) = 109

tera (T) = 1012

peta (P) = 1015

exa (E) = 1018

Power

1 h.p. (horsepower) = 745.7 W (watts) = 2.545 BTU/hr. = 550 ft.lb./sec.

1 ftlb/s = 1.356 W

1 J (joule) = 1 Nm = 107 ergs = 0.2389 cal.

1 W = 1 J/s

1 ev = 1.60219*10-19 J

1 erg = 10-7 J

Temperature

°F = [(°C*9)/5]+32, °C = Celsius (Centigrade), F = Fahrenheit

K = Kelvin

Rankine (R) = F - 459.666

0.252 calories = 1 BTU (British Thermal Unit)

-273.2 °C = -459.7 °F = 0 K = 0 R = absolute zero

0 °C = 32 °F = 273.3 K = 491.7 R = Water Freezes

100°C = 212°F = 373.3 K = 671.7 R = Water Boils (1 atm. pressure)

1 therm = 100,000 BTU

Mathematical

p radians = 3.1416 radians = 180 degrees = 0.5 cycles

1 Hz = 1 cycle/sec.

1 rpm (revolutions per minute) = 60 RPS (Revolutions per second) = 60Hz

1 fps (foot per second) = 1 ft/sec

1 mph (miles per hour) = 1 mi./hr.

1 cfm (cubic foot per minute) = 1 ft3/min.

e = 2.718

Time

1 Hz (hertz) = 1 s-1

1 year = 365 days = 52 weeks = 12 months

1 leap year = 366 days

1 day = 24 hours

1 fortnight = 14 days

1 hour = 60 min.

1 min = 60 seconds

1 millenium = 1000 years

1 century = 100 years

1 decade = 10 years

Physical Constants

R = 1.987 cal/mole K = ideal gas law constant

K = Boltzmann's constant = 1.3x10-16 erg/K = 1.3x10-23 J/K

h = Planck's constant = 6.62x10-27 erg-sec = 6.62x10-34 J.sec

Avagadro's number = 6.02x1023 atoms/atomic weight

density of water = 1 g/cm3

electron charge = 1.60x10-19 coul.

electron rest mass = 9.11*10**-31 Kg

proton rest mass = 1.67*10**-27 Kg

speed of light (c) = 3.00x1010 cm/sec

speed of sound in dry air 25 C = 331 m/s

gravitational constant = 6.67*10**-11 Nm**2/Kg**2

permittivity of free space = 8.85*10**-12 farad/m

permeability of free space = 1.26*10**-6 henry/m

mean radius of earth = 6370 Km

mass of earth = 5.98*10**24 Kg

Electromagnetic

magnetic flux = weber (We) = 10**8 maxwell

inductance = henry

magnetic flux density = tesla (T) = 10**4 gauss

magnetic intensity = ampere/m = 0.004*PI oersted

electric flux density = coulomb/m**2

capacitance = farad

permeability = henry/m

electric field strength = V/m

luminous flux = lumen

luminance = candela/m**2

1 flame = 4 foot candles = 43.05564 lux = 43.05564 meter-candles

illumination = lux

resistance = ohm