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Rayleigh's method of dimensional analysis
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Rayleigh's method of dimensional analysis : ウィキペディア英語版
Rayleigh's method of dimensional analysis
Rayleigh's method of dimensional analysis is a conceptual tool used in physics, chemistry, and engineering. This form of dimensional analysis expresses a functional relationship of some variables in the form of an exponential equation. It was named after Lord Rayleigh.
The method involves the following steps:
# Gather all the independent variables that are likely to influence the dependent variable.
# If ''R'' is a variable that depends upon independent variables ''R''1, ''R''2, ''R''3, ..., ''R''''n'', then the functional equation can be written as ''R'' = ''F''(''R''1, ''R''2, ''R''3, ..., ''R''''n'').
# Write the above equation in the form X = C X_1^a X_2^b X_3^c \cdots X_n^m \, where ''C'' is a dimensionless constant and ''a'', ''b'', ''c'', ..., ''m'' are arbitrary exponents.
# Express each of the quantities in the equation in some base units in which the solution is required.
# By using dimensional homogeneity, obtain a set of simultaneous equations involving the exponents ''a'', ''b'', ''c'', ..., ''m''.
# Solve these equations to obtain the value of exponents ''a'', ''b'', ''c'', ..., ''m''.
# Substitute the values of exponents in the main equation, and form the non-dimensional parameters by grouping the variables with like exponents.
Drawback – It doesn't provide any information regarding number of dimensionless groups to be obtained as a result of dimension analysis
== See also ==

* Physical quantity
* Buckingham pi theorem

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