Units of Measurement

Without units, communicating the measurement of something is impossible. Over the years, we have evolved from using barley grains arranged end to end to measure shoe size to having a definitive official kilogram stored in a vault in France against which all kilograms on earth are measured. In this section, we will list and explain the units of measurement used in CIBD lessons and how we use them.

System International (SI) units

At the CIBD, we use the SI system for our measurement units wherever possible. The table below shows the SI units you will encounter.

Table: SI units

SI UNIT NAME

SI UNIT SYMBOL

QUANTITY MEASURED

Ampere

A

Electric current

Degree Celsius

°C

Celsius temperature

Farad

F

Capacitance

Hertz

Hz

Frequency

Joule

J

Energy, work, quantity of heat

Joule per cubic metre

J/m3

Energy density

Joule per Kelvin

J/K

Heat capacity, entropy

Joule per kilogram

J/kg

Specific energy

Joule per kilogram Kelvin

J/kgK

Specific heat capacity

Kelvin

K

Absolute temperature – sometimes referred to as thermodynamic temperature

Kilogram

kg

Mass

Kilogram per cubic metre

kg/m3

Density, mass density

Metre

m

Length

Metre per second

m/s

Speed, velocity

Metre per second squared

m/s2

Acceleration

Mole

mol

Amount of substance

Newton

N

Force

Ohm

Ω

Electric resistance

Potential of hydrogen

pH

Acidity or alkalinity of water-soluble substances

Pascal

Pa

Pressure, stress

Second

s

Time or time interval

Volt

V

Electrical potential or potential difference, electromotive force

Watt

W

Power

SI Accepted UNIT NAME

UNIT SYMBOL

QUANTITY MEASURED

Minute

min

Time, 1 min = 60 s

Hour

h

Time, 1 h = 3,600 s

Day

d

Time, 1 d = 86400 s

Litre

L

Volume, 1 L = 0.001 m3

Tonne

t

Mass, 1 t = 1,000 kg

Bar

bar

Pressure

Dalton

Da

Atomic Mass

Poise

P

Absolute viscosity

SI Derived UNIT NAME

UNIT SYMBOL

QUANTITY MEASURED

Hectolitre

hL

volume, 1 hL = 100 L = 0.1 m3

Millilitre

mL

Volume, 1 mL = 1 cm3

Microlitre

μL

Volume, 1 μL = 1 mm3

Micron, Mircometre

μm

Length, 0.001 mm

Some units are derived from base units. In order to cancel them, we need to convert them to their base unit. The table below shows the ones you may encounter in Diploma lessons along with their base units.

Table: Derived SI units

Name

Symbol

Quantity

Equivalents

SI Base Unit Equivalent

newton

N

Force, weight

kg⋅m/s2

kg⋅m⋅s−2

pascal

Pa

Pressure, stress

N/m2

kg⋅m−1⋅s−2

joule

J

Energy, work, heat

m⋅N, C⋅V, W⋅s

kg⋅m2⋅s−2

watt

W

Power, radiant flux

J/s, V⋅A

kg⋅m2⋅s−3

volt

V

Voltage, electrical potential difference, electromotive force

W/A, J/C

kg⋅m2⋅s−3⋅A−1

ohm

Ω

Electrical resistance, impedance, reactance

1/S, V/A

kg⋅m2⋅s−3⋅A−2

 

Unit representation

We learned earlier that units can be written as fractions or as indices. For working with units in unit conversion and unit cancellation, it is easiest to show units as fractions. To convert between the two forms, you need to remember that x-1 is the same as 1/x, so J/kg is the same as J.kg-1. When the unit already has an exponent that is used in place of the 1. For example, in density kg/m3 we write it as kg,m-3. As with rates, the horizontal or diagonal line means per. So kg/m3 is kilograms per cubic metre. The -1 -2 or -3 also represent the word per.

Table: Three representations of commonly used units

Name of Unit

Unit as Indices

Unit as Single Line Fraction

Unit as a Fraction

Specific heat capacity

J. k g to the power of negative 1 end exponent degree C to the power of negative 1 end exponent

J divided by k g degree C

fraction numerator J over denominator k g degree C end fraction

Heat transfer coefficient

W. m to the power of negative 2 space end exponent K to the power of negative 1 end exponent

W divided by m squared K

fraction numerator W over denominator m squared K end fraction

Density

k g. m to the power of negative 3 end exponent

 k g divided by m cubed

fraction numerator k g over denominator m cubed end fraction

Volumetric flow rate

m cubed. h r to the power of negative 1 end exponent

 M cubed divided by h r

M cubed over h to the power of r

Mass flow rate

k g. h r to the power of negative 1 end exponent

k g divided by h r

fraction numerator k g over denominator h r end fraction

Specific energy

J. k g to the power of negative 1 end exponent

J divided by k g

fraction numerator J over denominator k g end fraction

Pressure

N. m to the power of negative 2 end exponent

N divided by m 2

N over m squared

Thermal conductivity

W m to the power of negative 1 end exponent K to the power of negative 1 end exponent

W divided by m K

fraction numerator W over denominator m K end fraction

Velocity

m. s to the power of negative 1 end exponent

m divided by s

m over s

 

Reciprocals effect on units

When we take a reciprocal of a number, its unit becomes inverted. For example, if we take a reciprocal of a heat transfer coefficient, the units change from:

h space equals space fraction numerator W over denominator m squared K end fraction

To:

fraction numerator 1 space over denominator h end fraction equals space fraction numerator m squared K over denominator W end fraction

Now we know our units and how they can be represented, we can start to make use of them. We do that next in unit conversion and cancellation.

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