Fully Developed Turbulent flow analytical soln?
Hi.
Is any way to analytically calculate the velocity profile between two plates in fully developed TURBULENT flow? THanks. 
Re: Fully Developed Turbulent flow analytical sol
(1). I don't think so. (2). But you can always try.

Re: Fully Developed Turbulent flow analytical sol
1) If we don't care about shear stress at the wall, is the velocity profile
u/u_0 = (y/ (h/2) )^(1/n) a good approximation for channel flow? 2) In this formula, where is the effect of pressure gradient along the channel?? Thanks. 
Re: Fully Developed Turbulent flow analytical sol
hi there,
You can refer to the following book: "VISCOUS FLUID FLOW" (2nd Edition) Frank, M., White McGrawHill, 1991. In the chapter 6 (Section 65.2), White proposes a formulation for the average velocity profile across the entire channel. I hope this helps. Sincerely, Frederic Felten CFD Laboratory. UT Arlington, TX, USA. http://utacfdb.uta.edu/ 
Re: Fully Developed Turbulent flow analytical sol
I came across a paper once which used mixing length and scaling arguments to come up with an closed form expression for the mean velocity profile in planar turbulent Couette flow.
I think the author's name is Noor but I am not sure. The profile compares fairly well with experiments but I doubt if you can call the method analytical given the assumptions that were used in its derivation. 
Re: Fully Developed Turbulent flow analytical sol
(1). It is just a curve fit. And n is normally a function of the Reynolds number, see Schlichting's Boundary Layer Theory book. (2).The curve fit is good for regions away from the wall, and if you apply the curve fit at the wall, the slope is singular there. (3). In other words, you can not evaluate the wall shear stress from this curve fit. Since the pressure gradient must be balanced by the wall shear stress in the fully developed flow (between the pressure gradient term and the diffusion term, no convection term contribution), the pressure gradient is unknown using this curve fit.

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