Chapter 2
Dimensional Analysis
“The result of a dimensional analysis of a problem is a reduction
of the number of variables in the problem” ...Henry Langhaar
(1951)
This chapter provides an introduction to the analytical technique referred to as dimensional analysis. Although consideration of the dimensions of physical properties have always been a factor in science and
engineering, it was not until the start of the 20th century that a structured analysis method based on dimensions was formalized. Ivicsics (1980)
credited Rjabushinsky and Buckingham with the development of the theory of dimensional analysis, and he stated that Rjabushinsky formulated
the fundamental concepts and Buckingham disseminated the theory in a
1914 publication. Contributors to the theory of dimensional analysis are
numerous, and several good texts are available that present concise and
formal mathematical treatment of the topic. The purpose of this chapter
is to provide a working knowledge of dimensional analysis for application
to engineering problems.
2.1 Dimensions
Before entering into a discussion of dimensional analysis it is beneficial to
review briefly some basic concepts of the dimensions of physical processes.
2.1.1 Physical Dimensions and Systems of Units
Dimensions and dimensional units are an integral part of every measurement of a physical property. Failure to include dimensional units in re
Dimensional Analysis
“The result of a dimensional analysis of a problem is a reduction
of the number of variables in the problem” ...Henry Langhaar
(1951)
This chapter provides an introduction to the analytical technique referred to as dimensional analysis. Although consideration of the dimensions of physical properties have always been a factor in science and
engineering, it was not until the start of the 20th century that a structured analysis method based on dimensions was formalized. Ivicsics (1980)
credited Rjabushinsky and Buckingham with the development of the theory of dimensional analysis, and he stated that Rjabushinsky formulated
the fundamental concepts and Buckingham disseminated the theory in a
1914 publication. Contributors to the theory of dimensional analysis are
numerous, and several good texts are available that present concise and
formal mathematical treatment of the topic. The purpose of this chapter
is to provide a working knowledge of dimensional analysis for application
to engineering problems.
2.1 Dimensions
Before entering into a discussion of dimensional analysis it is beneficial to
review briefly some basic concepts of the dimensions of physical processes.
2.1.1 Physical Dimensions and Systems of Units
Dimensions and dimensional units are an integral part of every measurement of a physical property. Failure to include dimensional units in re