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 X is a variable that depends upon independent variables X1, X2, X3, ..., Xn, then the functional equation can be written as X = F(X1, X2, X3, ..., Xn).
- Write the above equation in the form where C is a dimensionless constant and a, b, c, ..., m are arbitrary exponents.
- Express each of the quantities in the equation in some fundamental 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.
See also