Detailed Insights: Dimensions, Units and Conversions

Jennifer Fuentes

4 years ago

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Dimensions, units and conversions are essential for all chemical engineers and being able to go back and forth between different units will become second nature. It is vital for any chemical engineering student to get their head around this key concept.

Dimensions and Units

Understanding several dimensions is the most important first step and are as follows: Mass (M), Length (L) and Time (T), Amount of substance – Mole (mole), Electric current – Ampere (A) and temperature – Kelvin (K)

Having an understanding of these basics will help a lot when coming across quantities that look difficult to be able to give dimensions to.

Dimensions	Units
Length – used to locate the position of a point in space and so describe the size of a physical system	Kilometre, Metre, Foot, Inch
Time – conceived as a succession of events	Day, Hour, Minute, Second, Nanosecond
Mass – a measure of a quantity of matter	Kilogram, Pound, Ton, Tonne
Temperature – a measure of the energy of molecules in a system.	Degree Centigrade, Celsius, Kelvin, Rankin or Fahrenheit
Amount of a substance/molar amount	Mole
Electrical current	Ampere

Below is a table of quantities, dimensions and SI units – SI units are just a modern form of the metric system used by nearly every country apart from Myanmar, Liberia and the US.

Quantity	SI units	Dimensions
Mass	Kilogram	M
Length	Metre	L
Time	Second	T
Force	Newton	MLT^-2
Energy	Joule	ML²T^-2
Pressure	Newton/Square metre	ML^-1T^-2
Power	Watt	ML²T^-3

There is no point trying to remember dimensions as there are too many and it is time-consuming, the best way to understand it to use the equations that include the quantity

an example will be used to show this:

Example 1:

As seen in the above table the dimensions of force are given, can you show how they have got there?

Answer 1:

Force = mass x acceleration

We know that mass has dimensions of m, but what about acceleration?

Accelerations units are meters/second²

This has dimensions of length due to metres and dimensions of time due to seconds is T² as its seconds squared.

So, the dimension of acceleration is: L/T^-2

Thus, proving the dimensions of force are MLT^-2:

Force = mass x acceleration

Force = M x L/T^-2 = MLT^-2

Example 2:

what are the dimensions of density?

Answer 2:

The units for density are kg/m³ if you didn’t know this it’s fine you can work it out from the equation:

The equation for density is:

Density = mass/ volume

Mass is in kg and volume is in m³

The dimensions of mass we know is M, for the volume we know that volume is measured in meters (m³) and thus the dimensions would be L³.

Thus, the dimension of density is: ML^-3

Dimensional Equations

Dimensional equations are an easy way to be able to convert units and it can be done in three steps:

Step 1: Write out the given quantity and its units.

Step 2: Write in the units of conversion factors that will cancel out and replace the old units.

Step 3: Fill in the new values

Example 3:

Change the units from kg to g for 10m³/kg.

Answer 3:

1000 g = 1 kg

10 m3kg x (1kg1000 g) = 0.01 m3g

Hint: Always be careful about how you cancel your units and the best is to write it out, so you don’t make unnecessary mistakes.