Question

Reynolds number is a dimensionless number that is used in Fluid Mechanics to distinguish between the

laminar and turbulent flows particularly in pipes. Consider a pipe where the flowing fluid has the

following properties:

ρ is the density of the fluid (SI units: kg/m^3)

u is the velocity of the fluid with respect to the object (m/s)

D is pipe diameter (m)

μ is the dynamic viscosity of the fluid (Pa·s or N·s/m^2 or kg/m·s)

m is he mass of fluid in kg

Use Rayleigh’s method to derive the nondimensionalized group (called Reynold’s number) and show

that the non-dimensional group does not have any dimension.

Answer 1

Rayleigh's indicial Method is based on the fundamental principle of dimensional homogeneity of physical variables in a problem. In RIM, the dependent variable is expressed as a product of all the independent variables raised to sn unknown integer exponent.

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