Once again, this unit conversion technique shows its power by minimizing the number of conversion factors we must memorize. We need not memorize how many cubic inches are in a cubic foot, or how many square inches are in a square foot, if we know how many linear inches are in a linear foot and we simply let the fractions “tell” us whether a power is needed for unit cancellation.

Unity fractions are also useful when we need to convert more than one unit in a given quantity. For example, suppose a flowmeter at a wastewater treatment facility gave us a flow measurement of 205 cubic feet per minute but we needed to convert this expression of water flow into units of cubic yards per day. Observe the following unit-fraction conversion to see how unity fractions serve the purpose of converting cubic feet into cubic yards, and minutes into days (by way of minutes to hours, and hours to days):

Note how the only units left un-canceled on the left-hand side of the “equals” symbol are cubic yards (yd3) and days, which therefore become the units of measurement for the final result.

A major caveat to this method of converting units is that the units must be directly proportional to one another, since this multiplicative conversion method is really nothing more than an exercise in mathematical proportions. Here are some examples (but not an exhaustive list!) of conversions that cannot be performed using the “unity fraction” method:

•Absolute / Gauge pressures, because one scale is o set from the other by 14.7 PSI (atmospheric pressure).

•Celsius / Fahrenheit, because one scale is o set from the other by 32 degrees.

•Wire diameter / gauge number, because gauge numbers grow smaller as wire diameter grows larger (inverse proportion rather than direct) and because there is no proportion relating the two.

•Power / decibels, because the relationship is logarithmic rather than proportional.

The following subsections give sets of physically equal quantities, which may be used to create unity fractions for unit conversion problems. Note that only those quantities shown in the same line (separated by = symbols) are truly equal to each other, not quantities appearing in di erent lines!

2.4.2Conversion formulae for temperature

Note: all of the conversion factors given for temperature are exact, not approximations.

oF = (oC)(9/5) + 32 oC = (oF − 32)(5/9) oR = oF + 459.67

K = oC + 273.15

2.4.3Conversion factors for distance

Note: all of the conversion factors given for distance are exact, not approximations.

1 inch (in) = 2.54 centimeters (cm)

1 foot (ft) = 12 inches (in)

1 yard (yd) = 3 feet (ft)

1 mile (mi) = 5280 feet (ft)

2.4.4Conversion factors for volume

Note: all conversion factors shown in bold type are exact, not approximations.

1 gallon (gal) = 231.0 cubic inches (in3) = 4 quarts (qt) = 8 pints (pt) = 16 cups = 128 fluid ounces (fl. oz.) = 3.7854 liters (l)

1 milliliter (ml) = 1 cubic centimeter (cm3)

2.4.5Conversion factors for velocity

Note: all conversion factors shown in bold type are exact, not approximations.

1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) = 1.60934 kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 knot (knot – international)

2.4.6Conversion factors for mass

1 pound-mass (lbm) = 0.4535924 kilogram (kg) = 0.031081 slugs

2.4.7Conversion factors for force

1 pound-force (lbf) = 4.448222 newtons (N)

1 kilogram-force (kgf) = 9.80665 newtons (N)

2.4.8Conversion factors for area

Note: all conversion factors shown in bold type are exact, not approximations.

1 acre = 43560 square feet (ft2) = 4840 square yards (yd2) = 4046.86 square meters (m2)

2.4.9Conversion factors for pressure (either all gauge or all absolute)

Note: all conversion factors shown in bold type are exact, not approximations.

1 pounds per square inch (PSI) = 2.03602 inches of mercury at 0 oC (in. Hg) = 27.6799 inches of water at 4 oC (in. W.C.) = 6.894757 kilopascals (kPa) = 0.06894757 bar

1 bar = 100 kilopascals (kPa) = 14.504 pounds per square inch (PSI)

1 meter of water at 4 oC (m W.C.) = 9.80665 kilopascals (kPa)

2.4.10Conversion factors for pressure (absolute pressure units only)

Note: all conversion factors shown in bold type are exact, not approximations.

1 standard atmosphere (Atm) = 14.7 pounds per square inch absolute (PSIA) = 101.325 kilopascals absolute (kPaA) = 1.01325 bar absolute = 760 millimeters of mercury absolute (mmHgA) = 760 torr (torr)

2.4.11Conversion factors for energy or work

1 British thermal unit (Btu – “International Table”) = 251.996 calories (cal – “International Table”) = 1055.06 joules (J) = 1055.06 watt-seconds (W-s) = 0.293071 watt-hour (W-hr) = 1.05506 x 1010 ergs (erg) = 778.169 foot-pound-force (ft-lbf)

2.4.12Conversion factors for power

Note: all conversion factors shown in bold type are exact, not approximations.

1 horsepower = 550 foot-pounds per second (ft-lbf/s) = 745.7 watts (W) = 2544.43 British thermal units per hour (Btu/h) = 0.0760181 boiler horsepower (hp – boiler)

2.4.13Terrestrial constants

Acceleration of gravity at sea level = 9.806650 meters per second per second (m/s2) = 32.1740 feet per second per second (ft/s2)

Atmospheric pressure = 14.7 pounds per square inch absolute (PSIA) = 760 millimeters of mercury absolute (mmHgA) = 760 torr (torr) = 1.01325 bar (bar)

Atmospheric gas concentrations (by volume, not mass):

•Nitrogen = 78.084 %

•Oxygen = 20.946 %

•Argon = 0.934 %

•Carbon Dioxide (CO2) = 0.033 %

•Neon = 18.18 ppm

•Helium = 5.24 ppm

•Methane (CH4) = 2 ppm

•Krypton = 1.14 ppm

•Hydrogen = 0.5 ppm

•Nitrous Oxide (N2O) = 0.5 ppm

•Xenon = 0.087 ppm

Density of dry air at 20 oC and 760 torr = 1.204 mg/cm3 = 1.204 kg/m3 = 0.075 lb/ft3 = 0.00235 slugs/ft3

Absolute viscosity of dry air at 20 oC and 760 torr = 0.018 centipoise (cp) = 1.8 × 10−5 pascalseconds (Pa·s)

2.4.14Properties of water

Freezing point at sea level = 32 oF = 0 oC

Boiling point at sea level = 212 oF = 100 oC

Density of water at 4 oC = 1000 kg/m3 = 1 g/cm3 = 1 kg/liter = 62.428 lb/ft3 = 1.94 slugs/ft3

Specific heat of water at 14 oC = 1.00002 calories/g·oC = 1 BTU/lb·oF = 4.1869 joules/g·oC Specific heat of ice ≈ 0.5 calories/g·oC

Specific heat of steam ≈ 0.48 calories/g·oC

Absolute viscosity of water at 20 oC = 1.0019 centipoise (cp) = 0.0010019 pascal-seconds (Pa·s) Surface tension of water (in contact with air) at 18 oC = 73.05 dynes/cm

pH of pure water at 25 oC = 7.0 (pH scale = 0 to 14 )