The Re number is a dimensionless number indicating the ration of inertial to viscous forces or stresses. 

Terms for inertial and viscous stresses are (ρV2) and (μV / L) respectively. Where V and L denote velocity and characteristic length. By dividing these two terms the Re number will appear.

The point is in the viscous stress term; L. This term is the Newton's law of viscosity. So the characteristic length is the parameter that creates the variable velocity profile and shear stress accordingly. This parameter for flow in a tube is the tube's diameter. We see that by changing the diameter the profile will change. 

@ Ali Mehrasa,  thanks a lot, this makes sense.....

@ Ali Mehrasa , one doubt in that case. Since characteristic length is the parameter that creates the variable velocity profile and shear stress, why then for a cylinder it is taken as diameter and not the length( over which the boundary layers are formed) ?

The average velocity of a flowing fluid, for a given mass flow rate, is a strong function of  diameter; in general the area of cross section of the flow channel.  For a non-circular sections the equivalent diameter is used in the calculations of Re.  

Effect of length on velocity is not significant.   

Pl refer the Dimensional Analysis chapter.  

Dear Rajesh I'm so glad my answer helped you.

By assuming the length of a cylinder as characteristic length, there will be different Re numbers for a particular fluid flow condition. Suppose a flow in which we know the density, viscosity, and velocity of the fluid. If we set the cylinder length as characteristic length, we will get different Re numbers by changing the cylinder length. While we know the length of the cylinder has no effect on developed flows. So this assumption is incorrect.

If change in characteristic length makes no difference in flow, obviously it won't be the right choice.

Regards

Hello, I am studying flow around two elliptic particles of different dimensions. Normally the Reynolds number is based on the length of the major axis or the hydraulic diameter. But in my case the particles have different dimensions. Please guide me in case of the length that should be used to calculate the Reynolds number.

I do not know if this will help. But you might want to think about the acoustic modes in the fluid, gas or plasma you are observing. The interaction with whatever surfaces are nearby generates shocks (or impulses, or solitons, or wavelets, or wave sources - lots of names and descriptions out there) which propagate at near the local sound velocity (density, temperature, and molecular rotational and vibrational states affect the speed of propagation of energy, momentum, mass and specific particles). The waves reflect from the surfaces, and can interfere within the body of the fluid if there are viscous (bending, scattering, shear, refraction) divergence from simple rays. When the fluid flow is such that modes of the standing waves (see also eigenmodes, eigenfrequencies) are excited, then there can be collective changes across the whole flow, not just in small regions. I suppose you can think of 3D Voronoi cells and then treat the boundary conditions if you want to cover the whole spectrum of internal characteristic length scales. A cell can be broken into finer and finer cells. Choosing Voronoi internal points at random, according to real statistics, should generally converge to fit the data, when you have many sensors intercorrelated. I haven't had a chance to check that, but I am pretty sure it should work. You might guess that I am encouraging you to get serious, try harder problems, and treat each problem completely. When I look at fluid flow in a pipe, I consider the whole physical, economic, social and financial context as well.

The ρV^2 is an energy density (Joules/meter^3). The pressure can be considered the same way, Newton*meter/(meter^2 *meter). When a coherent structure (mode, state, correlated region, again lots of names) dissipates in a short distance, we take note and try to remember the distance over which the kinetic energy scatters to smaller scales and looks like something else. The coherent, observable motion of a fluid parcel gets broken into smaller "eddies" and ultimately into thermal motion in the fluid. The laser pulse scatters repeatedly until it is completely absorbed in a random media. Many of these problems can at least be approached by transforming to acoustic or optical models. The Reynolds number is trying to help you estimate or predict the future or common behavior of a system. If you have a more complex or different set of starting points, then try lots of different models until you find one that will help. Better yet, find some real data, or collect some, and ponder its meaning. I would be measuring the acoustic signatures of the flow at various points, scattering of light from small density fluctuations, and scattering of light or sound from the molecules of the fluid itself. Going down one level in scale gives you only a small probability of finding a permanent answer. Most people have to go down many orders of magnitude in length scale to at least molecular scale; not counting infrared, THz, and other electromagnetics, magnetic field variations and gravity changes at the location. Every atom or molecule or electron is ultimately unique because of its history and context. I guess I am saying that one or two numbers is not enough information to capture the motion of billions of Avagadro's number of particles, let alone acoustic modes and their variations in a real fluid flow.

Sorry to interrupt. Best wishes

Richard Collins, The Internet Foundation

It helps in Similitude.