# 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
*R*=*C**R*_{1}^{a}*R*_{2}^{b}*R*_{3}^{c}...*R*_{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

## References

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