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 R1, R2, R3, ..., Rn, then the functional equation can be written as R = F(R1, R2, R3, ..., Rn).
- Write the above equation in the form R = C R1a R2b R3c ... Rnm, 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