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Dimensional analysis is based on representing physical quantities with a combination of fundamental dimensions, noting that units of two sides of an equation must be consistent.

In fluid mechanics, as in other branches of engineering sciences, the fundamental dimensions are mass (M), length (L), and time (T). Temperature, if applicable, can be assigned a fundamental dimension such as (θ). These fundamental dimensions can be used to provide qualitative descriptions of physical quantities: for example, velocity can be described as LT⁻¹, density as MT⁻³, and so on. Table 1.2 lists the symbols, units, and dimensions of common physical quantities. For effective application of dimensional analysis, it is essential to state which independent variables are relevant to the problem.

Table 1.2 Symbols, units, and dimensions of common physical quantities.

Quantity	Symbol	Units	Dimensions
Length	l	m	L
Time	t	s	T
Mass	m	kg	M
Force	F	N	MLT −2
Temperature	T	K	θ
Velocity	C or V	m/s	LT −1
Volume	m 3	m 3	L 3
Acceleration	a	m/s2	LT −2
Angular velocity	ω	rad	T −1
Area	m 2	m 2	L 2
Volume flow rate		m3/s	L 3 T −1
Mass flow rate		kg/s	MT −1
Pressure	p	N/m2	ML −1 T −2
Density	ρ	kg/m3	ML −3
Specific weight	γ	N/m3	ML −2 T −2
Dynamic viscosity	μ	N. s/m2	ML −1 T −1
Kinematic viscosity	ν	m2/s	L 2 T −1
Work	W	J	ML 2 T −2
Power		W	ML 2 T −3
Surface tension	σ	N/m	MT −2
Bulk modulus	B	N/m2	ML −1 T −2
Momentum	G	kg. m/s	MLT −1
Torque, moment of force	T, M	N. m	ML 2 T −2

In cases where temperature is a basic physical quantity and it is preferable to avoid using an extra fundamental dimension such as θ, the gas constant is usually lumped together with the temperature, and the combined variable RT = p/ρ (from the equation of state) will have the dimensions