Dear Modhuchandra Laishram,

the Reynolds number allows you to compare flow systems with 'normal' uncharged fluids. E.g. for the comparison how water will behave in two different pipes. Then the flow will show the same behavior at same Reynolds numbers (e.g. when the turbulence will set in). The dynamics will be the same, but the absolute numbers will differ when the pipes have different diameters.

In case you are dealing with a plasma the Reynolds number is not sufficient to characterise the system. Depending on the system beta, Maxwell number etc. can come into play.

Best regards,

Hans Werner Müller

Dear Hans Werner Müller, thank you very much for your response . Its helpful but still have some doubt regarding absolute no. in your explanation. Will you please explain what is absolute  no. and how it differ from Reynolds no. ?? And why Reynold no. can not significant in charge system??

What Hans Werner meant is that the Reynolds number is an absolute number, i.e. it has no physical dimension (like m, kg, ...) attached to it.

A plasma usually is treated as a charged fluid, which means that you have an additional physical parameter (at least one): the charge. The classical Reynoldsnumber only consists of entities without any charging (as in the example of water running through a pipe). So, if you deal with the classical Reynoldsnumber the charge does not play any role but in a plasma charges also have to be considered. Hence the Reynolds number will be not enough to describe a plasma.

Dear sir, Please forget about the charge and plasma , my simple doubt is that.... suppose i am observing neutral fluid flow in two system of different dimension, say small pipe and large pipe, accordingly velocity also found to be different. However when i calculated the (Rn= UL / mu) , both system give the same value. Then may i confirmed that both system has same Dynamical nature ????

So, what you are telling us is that you did not change the viscosity of your fluid, you did not change the characteristic length of your pipe but you changed the flow velocity in your equation and get still the same result? - Than you simply have a calculation error.

Or do you have an extremly compressable fluid? - this can change the viscosity greatly, if the flow velocity changes.

dear Johannes Gruenwald ,  i am asking you very simple question regarding Rn=U*Lr/mu, for incompressible fluid and  \mu is const.  Suppose for small pipe Lr is small but U is large, and for large pipe Lr is large and U is small, but the calculated Rn is found to be same in both case. What implies by this observation,?? Is the flow nature same at all Rn value.??????  thank you.

So, first of all: if you want to have a good answer to a question, you have to ask a good question, which means that you should mention from the beginning, for example, if the fluid is compressible or not, if it is charged (plasma) or not, ...

Secondly, if the question is very simple, you should have figured out the answer by yourself, up to now, shouldn't you?????????????

When you take an incompressible fluid in a pipe with samll diameter d_s and another pipe with large diameter d_l. The viscosity should be the same in both systems (same fluid). Then you will observe that in both cases turbulence sets in at about Re=2300. This requires a higher velocity at smaller radius. But you must be aware that we talk about the diameter averaged mean velocity.

Two different systems (e.g. different size) will deliver the same answer when they show the same Re number. The art is to define the adequate characteristic length of the system when the geometry is getting more complex.

The concept of the Re number is also useful to trasnlate the result not only from one pipe system to another but also to do measurements in oe fluid and to translate the result to another one. Same behaviour at same Re number.

Best wishes.

Dear Hans Werner Müller , i feel you have clear my doubt. thank you.