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).