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 | ML^{2}T^{-2} |
Pressure | Newton/Square metre | ML^{-1}T^{-2} |
Power |
Watt | ML^{2}T^{-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?
Example 2:
what are the dimensions of density?
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 10m^{3}/kg.
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.