1 Dimensions

What do we mean by a ‘dimension’? The distance between two points, say Exeter and London, can be measured in many units : metres, miles, yards, chains, cubits, barleycorns, parsecs . . . however the quantity distance is a measure of length, no matter what units we use to measure it in. We say that this quantity has dimensions of length. Square brackets [] are often used to denote dimensions, so we can say that

the diameter of a pipe [d] has dimensions of length, [L]

The speed, say of a train, can be measured in units of kilometers per hour, metres per second or, (on a bad day) possibly inches per hour. In all cases these refer to a particular dimensional property, speed. We could invent a symbol for this property, say [S]. In fact, we choose to represent it in terms of two base dimensions, [L] (which we have already met) and time [T]. Thus

velocity [v] has dimensions [LT -1]

In the metric system, we have 7 basic dimensional quantities :

Length: - [L], measured in metres
Mass: - [M], measured in kilograms
Time: - [T], measured in seconds
Temperature: - [], measured in kelvins
Electrical current: - [I], measured in ampéres
Number: - [N] (generally of atoms), measured in moles
Luminous intensity: - [C], measured in candela

The dimensions of all other quantities can be derived from this basic set. In fluid dynamics, only the first three are really important, although the temperature might appear in problems involving heat transfer, or the current for magnetohydrodynamical problems.

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