Fundamentals of Heat Engines. Jamil Ghojel

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Analysis

      Many problems in fluid mechanics can be solved analytically; however, in a large number of cases, problems can only be solved by experimentation. Similitude and dimensional analysis make it possible to use measurements obtained in a laboratory under specific conditions to describe the behaviour of other similar systems without the need for further experimentation.

      1.2.4.1 Dimensional Analysis

      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 Скачать книгу