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Dimensions and Units in Fluid Mechanics
- A dimension is a measure of a physical variable.
- In fluid mechanics, there are four primary dimensions: mass, length, time, and temperature. Primary dimensions are defined as independent dimensions, from which all other dimensions can be obtained. They are listed below, along with their symbols.
| Dimension | White's symbol | Cimbala's symbol |
|---|
| Mass | M | m |
| Length | L | L |
| Time | T | t |
| Temperature | q | T |
- All other dimensions in fluid mechanics (called secondary dimensions) can be constructed from combinations of these four primary dimensions.
- It is customary to use brackets around a variable to indicate its dimensions. For example "{Power}" means "the dimensions of power."
- Example - Dimensions of Force - Force is not a primary dimension in fluid mechanics. Yet, force (and any other secondary dimension used in fluid mechanics) can be written as a combination of the four primary dimensions, i.e. in terms of mass, length, time, and temperature.
- Example - Dimensions of Power - Power is not a primary dimension in fluid mechanics. Yet, power (and any other dimension used in fluid mechanics) can be written as a combination of the four primary dimensions, i.e. in terms of mass, length, time, and temperature.
- Dimensions have no numbers associated with them.
- A unit is a way to assign a number or measurement to a dimension.
- There are three primary unit systems in use:
- the International System of Units (SI units - kg, N, m, s, K)
- the English Engineering System of Units (commonly called English units - lbm, lbf, ft, s, R)
- the British Gravitational System of Units (BG - slug, lbf, ft, s, oR)
- Units must always have numbers associated with them.
- For example, length is a dimension, but it is measured in units of feet (ft) or meters (m).
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