velocity as function of diameter in turbulent flow ? 1

[CARF]

Dear all,

In my very old school book I found this equation to describe "velocity as function of diameter in laminar flow":

Vposition = 2 * Vavg * (1-(r^2/R^2)) ; where r = distance from the pipe centre and R = pipe radius. This results in a nice parabolic velocity profile (as can be expected for laminar flow).

My question is: do you have an equation like that for turbulent flow?

Help is much appreciated !

Kind regards,
MVD

 

[SooCS]

For turbulant flow, the velocity is the same anywhere within the straight pipe.

 

[CARF]

Dear SooCS,

Not quite, the flow profile will NOT be parabolic, but more flat. Does anybody know the correct equation?

 

[hacksaw]

Correlations do exist the flow profile. Are they any good? It depends on how much straight run you have. That actual profiles will be considerably different depending on the pipe size and the fluid state. You'll have to consult the fluids literature for the recommended exponents.

Ultimately, where the profile is critical, you have to perform a in-situ profile measurement.

 

[CARF]

Could't agree more! However I need this equation for turbulent flow (if only an estimate) to finish my web-site pressure drop calculator.

follow this link to see what I mean ->

http://home.hccnet.nl/m.dijk/pressure_drop_calculator/

Please?

 

[25362]

One book I have says that the velocity profile is quite flat in turbulent flow, and that the average velocity V_ave = v_max/1.2 (for laminar flow V_ave= v_max/2) .

The thickness of the wall laminar layer that offers resistance to heat and mass transfer decreases with increasing Reynolds number, from 0.0043r at Re=10,000 to 0.00055r at Re = 100,000. r is the internal radius of the pipe or circular tube.

 

[saxon]

Just too add a little wrinkle to this discussion, don't forget to add the "Transitional" flow regime (Re=approx. 2000 to 4000)where the flow can be either laminar or turbulent or flip/flopping back and forth, dependant on position in the flow system.

saxon

 

[CARF]

Dear all, I found the answer in an even older book =>

A fairly simple equation that isn't too bad is:

Vposition = Vc (1 - r/R)^(1/n)

Vc is centerline velocity. n is a function of the Reynolds number. Varies from about 6 to 10. Specific values: n=7 for Re=10^5, n=9 for Re=10^6. More or less linear variation
on plot of n vs. log Re.

Any comments?

 

[RWF7437]

Here's a link that might help too.

http://www.care.auckland.ac.nz/~cchr010/courses/adfluids/f2m02.pdf

 

[CARF]

Great text!

Thanks,
Mark