How the Reynold number of 4000 consist of laminar flow?

[Waqar Amin]

I was asked a question that the Reynold number of a fluid is greater than 4000 but flow Is Still laminar. How is it possible? can anyone explain?.

 

[boneh3ad]

Is this a pipe flow? If it is an open flow like over an airfoil then the Reynolds number based on downstream distance (\mathrm{Re}_x) is typically in the millions before transition occurs. For pipe flow, the diameter Reynolds number (\mathrm{Re}_D)is usually closer to 2300 at transition. The only way I can think of for a pipe to have a higher transition Reynolds number is if it was perfectly smooth or they were using some unconventional length scale such as circumference.

 

[Waqar Amin]

Thanx boneh3ad :)
is this also possible for a smooth pipe having very large diameter?

 

[boneh3ad]

For a pipe flow, the characteristic length is usually the diameter already so the transition Reynolds number is independent of diameter. That is the beauty of nondimensional numbers. I misspoke earlier; the actual typical onset of transition is around 2300. You can theoretically delay this as you make the wall smoother. However, 4000 is really pushing it since that is typically not even considered transitional but a fully turbulent area so you would really need some sort of perfectly smooth pipe.

 

[HengHY]

what kind of fluid?

 

[boneh3ad]

what kind of fluid?

That doesn't matter as long as it is Newtonian and not rarefied.

 

[Studiot]

Laminar at R_e = 4 x10³ ?

That's not very high even for pipes.

Reynolds' original experiments noted

"The transistion was sensitive to the entry conditions and with special precautions laminar flow is maintained at R_e to beyond 2x10⁴ at least for distances up to 100 pipe diameters"

An Experimental Investigation of Circumstances which Determine whether the motion of water shall be Direct or Sinuous..."
Phil. Trans. Roy. Soc. 1883

He also observed the lower limit of R_e =2.3 x 10³ for large distances down the pipe.

This figure reappears in the construction of the Moody diagram (you should look this up)
which implies a pipe friction factor of <0.012
for laminar flow at R_e = 4 x 10³
Proc. Roy.Soc. vol91, p46, 1915.

 

[boneh3ad]

Where does it say that anywhere in Reynolds' paper? He didn't call it the Reynolds number, so I know for a fact that he didn't use "Re" in the paper anywhere. I have his paper in front of me and I don't see anywhere mention of specific values of the Reynolds number (which he refers to only as \frac{\rho c U}{\mu}). Were you referring to a line in another paper that cites Reynolds original paper or am I just missing something?

Meanwhile, any fluid mechanics textbook covering pipe flow will tell you that pipe flows are usually doomed to become turbulent starting in the range 2300\leq\mathrm{Re}_D\leq4000. Of course laminar flow is maintained for some distance downstream because the pipe still has to go through the transition process, but the general rule is that depending on the pipe roughness, that is the range of \mathrm{Re}_D you expect before the flow will eventually transition. On the low end of that range the pipe will transition quite far downstream.

This actually isn't in contradiction to what you just said about having laminar flow present as high as \mathrm{Re}_D = 2 \times 10^4 because all your quote says is that laminar flow is maintained at least up to 100 pipe diameters, implying that it does still eventually transition as predicted by the common rule of thumb. Pipe flow is perhaps the only flow that follows such a simple rule of thumb like this that we know of.

 

[Studiot]

He also observed the lower limit of Re =2.3 x 103 for large distances down the pipe.

Sorry I should have made this more clear, this lower limit is the limit below which induced turbulent flow dies out if the pipe is long enough.

 

[Waqar Amin]

Thanx to all for helping me. :)
but I have confused now and i think my concept about reynolds number is very weak yet. can anyone post a link here which explain and elaborate the concept of reynold number very clearly beyond conventional statements and it dependence on different parameters and nature of materials.