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CHAPTER 2. DIMENSIONAL ANALYSIS
of a phenomenon revealed, by dimensional reasoning alone.
(Laugh aar 1951).
In the last sentence, Langhaar cautioned against putting too much stock in
the results of a dimensional analysis because it provides no physical insight.
Murphy (1950) also offered a cautionary note when he said:
In itself, dimensional analysis gives qualitative rather than quantitative relationships, but when combined with experimental procedures it may be made to supply quantitative results and accurate prediction equations.
Others have taken a less enthusiastic approach about dimensional analysis. Le Méhauté (1990) described dimensional analysis as "... a poor substitute for theory, which is able to group successfully a few experimental variables when the phenomenon is too complex to resort to a more theoretical
approach.” Le Méhauté concedes, however, that “In the study of extremely
complex problems with theoretical difficulties, it [dimensional analysis] may
be the only possible approach to classify experimental results.” Thus, the experimenter should be aware of the method of dimensional analysis, because
in many cases some of the arbitrariness that arises from dimensional analysis can be resolved with some inspection and thought about the physical
processes (Le Méhauté 1990).
Despite its shortcomings, dimensional analysis has become an important
mathematical tool of experimenters. Hudson, et al. (1979) summed it up
nicely when they said that the best method for solving coastal problems is
by direct solution of the governing differential equations. However, when
this is not possible, which is often the case, the method of dimensional
analysis can be used to great advantage.
Murphy (1950) listed several applications for dimensional analysis:
1. Classifying equations and determining their generality.
2. Converting equations or data from one system of units to
another.
3. Developing equations in terms of process variables.
4. Systematizing the collection of data in an experimental
program and reducing the number of variables which must
be investigated.
5. Establishing the principles of model design, operation, and
interpretation.
Some of Murphy’s applications will become more apparent once the inner
workings of dimensional analysis are examined in greater detail.
CHAPTER 2. DIMENSIONAL ANALYSIS
of a phenomenon revealed, by dimensional reasoning alone.
(Laugh aar 1951).
In the last sentence, Langhaar cautioned against putting too much stock in
the results of a dimensional analysis because it provides no physical insight.
Murphy (1950) also offered a cautionary note when he said:
In itself, dimensional analysis gives qualitative rather than quantitative relationships, but when combined with experimental procedures it may be made to supply quantitative results and accurate prediction equations.
Others have taken a less enthusiastic approach about dimensional analysis. Le Méhauté (1990) described dimensional analysis as "... a poor substitute for theory, which is able to group successfully a few experimental variables when the phenomenon is too complex to resort to a more theoretical
approach.” Le Méhauté concedes, however, that “In the study of extremely
complex problems with theoretical difficulties, it [dimensional analysis] may
be the only possible approach to classify experimental results.” Thus, the experimenter should be aware of the method of dimensional analysis, because
in many cases some of the arbitrariness that arises from dimensional analysis can be resolved with some inspection and thought about the physical
processes (Le Méhauté 1990).
Despite its shortcomings, dimensional analysis has become an important
mathematical tool of experimenters. Hudson, et al. (1979) summed it up
nicely when they said that the best method for solving coastal problems is
by direct solution of the governing differential equations. However, when
this is not possible, which is often the case, the method of dimensional
analysis can be used to great advantage.
Murphy (1950) listed several applications for dimensional analysis:
1. Classifying equations and determining their generality.
2. Converting equations or data from one system of units to
another.
3. Developing equations in terms of process variables.
4. Systematizing the collection of data in an experimental
program and reducing the number of variables which must
be investigated.
5. Establishing the principles of model design, operation, and
interpretation.
Some of Murphy’s applications will become more apparent once the inner
workings of dimensional analysis are examined in greater detail.