Units and Dimensions - What are the differences

A car is moving at 100 miles per hours. How many minutes it takes to go from A to B, distant 345 kilometers?

Almost every problem in engineering incorporates, at some moment, units and dimensions. And one of the main sources of error in simple calculations comes from using different units when performing calculations. For instance, in the example of the car above, it is clear that it moves at a rate of 100 miles per hours meaning that:
In 1 hour, it covers 100 miles.
In 2 hours it covers 200 miles.
In 3 hours, 300 miles and so on.

But how to know how long it will take for the car to cover the distance of 345 kilometers. Miles and kilometers are two among several units used to measure a dimension called length. Other units are meter, inches, feet and the list goes on…

So let us define what is a dimension. According Himmelblau (2012), dimension is a physical quantity such as length, time, mass, temperature and so on. They may be subdivided into basic dimensions and derived dimensions.

• Basic dimensions are independent physical quantities, which are enough to describe essential physical quantities. E.g length.

• Derived dimensions are those which can be expanded in terms of basic dimensions. E.g volume.

Units are ways of expressing dimensions in quantities. For instance, 1 meter represents a certain amount of the dimension length. Or 1^o C represents a temperature value. The following table provides a summary of some dimensions and units commonly used in engineering. All the units are according the International System of Units (SI).

Dimension	Unit Name	Unit symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	Kelvin	K
Energy	Joule	J
Power	Watt	W
Density	kilogram per cubic meter	kg.m^-3
Velocity	meter per second	m.s^-1

Reference:
Himmelblau, D. M., & Riggs, J. B. (2012). Basic principles and calculations in chemical engineering.

Until the next post!