Units Conversion By Factor-label - The Factor-label Method For Converting Units

The Factor-label Method For Converting Units

The factor-label method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained. For example, 10 miles per hour can be converted to meters per second by using a sequence of conversion factors as shown below:

10 mile 1609 meter 1 hour meter -- ---- × ---- ----- × ---- ------ = 4.47 ------ 1 hour 1 mile 3600 second second

It can be seen that each conversion factor is equivalent to the value of one. For example, starting with 1 mile = 1609 meters and dividing both sides of the equation by 1 mile yields 1 mile / 1 mile = 1609 meters / 1 mile, which when simplified yields 1 = 1609 meters / 1 mile.

So, when the units mile and hour are cancelled out and the arithmetic is done, 10 miles per hour converts to 4.47 meters per second.

As a more complex example, the concentration of nitrogen oxides (i.e., NOx) in the flue gas from an industrial furnace can be converted to a mass flow rate expressed in grams per hour (i.e., g/h) of NOx by using the following information as shown below:

NOx concentration
= 10 parts per million by volume = 10 ppmv = 10 volumes/106 volumes
NOx molar mass
= 46 kg/kgmol (sometimes also expressed as 46 kg/kmol)
Flow rate of flue gas
= 20 cubic meters per minute = 20 m³/min
The flue gas exits the furnace at 0 °C temperature and 101.325 kPa absolute pressure.
The molar volume of a gas at 0 °C temperature and 101.325 kPa is 22.414 m³/kgmol.
10 m³ NOx 20 m³ gas 60 minute 1 kgmol NOx 46 kg NOx 1000 g g NOx --- ------ × -- ------ × -- ------ × ------ --------- × -- --------- × ---- -- = 24.63 ----- 106 m³ gas 1 minute 1 hour 22.414 m³ NOx 1 kgmol NOx 1 kg hour

After cancelling out any dimensional units that appear both in the numerators and denominators of the fractions in the above equation, the NOx concentration of 10 ppmv converts to mass flow rate of 24.63 grams per hour.

Read more about this topic:  Units Conversion By Factor-label

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