Rayleigh's Ritz Method

RAYLEIGH'S RITZ METHOD

This method was proposed by Rayleigh in the year 1899 in order to determine the effect of temperature on the viscosity of a gas. In this method, the fundamental relationship of some variables are expressed in the form of an exponential equation, which must be dimensionally homogeneous.

In this method, the expression is determined for a variable depending upon maximum three (or) four variables only. If the number of independent variables, becomes more than four, it is very difficult to find the expression for the dependant variables.

1. Steps Involved in Rayleigh's Ritz Method.

Step - 1:

Write the fundamental relationship of given dependant and independent variables. 

Consider X as dependent variable which depends on X1, X2, X3....Xn as independent variables.

Functional Equation X = ƒ (X1, X2, X3....Xn)

Step - 2:

The functional equation is expressed in terms of arbitary powers a, b, c... z

Hence

where

k - constant

a, b, c... z – Arbitary powers

Step - 3:

The values of a, b, c ... z are determined with the help of dimensional homogeneity. It means the power of the fundamental dimensions on both sides are compared to obtain the values of exponents.

Step - 4:

The values of exponents power (a, b, c... z) are substituted in the functional equation and simplified to obtain the suitable form.