RALEIGH METHOD

A basic method to dimensional analysis method and can be simplified to yield dimensionless groups controlling the phenomenon.

                              

For summary, the procedures of Raleigh method are;

Example 1:

Express dimensionless equation for the speed V with a wave pressure travels through a fluid. Consider the physical factors probably influence the speed are compressibility, E_v (or K), density, ρ and kinematics viscosity, ν.

                                           

Answer:

Using F, L, and T as primary units,      

Equating the powers of F, L, and T on both sides,

For F:  1 = c + d                         (1)

For L:  0 = a + b – 4c – 2d       (2)

For T:  0 = -b + 2c d                  (3)

Since there are three equations and four unknowns, three variables can be expressed in terms of the fourth using substitution method.

From (1) c = 1 – d

From (3) b = 2c + d = 2 – d

From (2) a = -b + 4c + 2d = - (2 – d) + 4 – 4d + 2d = 2 – d

   

     

EXAMPLE 3 : The velocity of propagation of a pressure wave through a liquid can be expected to depend on the elasticity of the liquid represented by the bulk modulus K, and its mass density ρ. Establish by D. A. the form of the possible relationship.