caculation of friction factor
hi everybody,
I know this is pretty simple question to experts here. But i find variable results in calculating average friction factor and nusselt number in turbulent flow through sinusoidal duct. Friction factor in a duct is calculated by f = (dp/dz)*hydraulic_diameter/(0.5*density*mean_vel**2). Now to calculate average friction factor for a length L, (1) can i approximate dp/dz=(mean_pres_at2mean_pres_at1)/L? (2) can i calculate mean pressure at any cross section by, mean_pres_at1=sum(pres.dA)/A1? Would it be same for separated region? Is there any better way to calculate overall friction factor and nusselt number from pressure, velocity and temperature field?? Thanks in advance for your help. Dilip 
Re: caculation of friction factor
(1). You need to go back to the momentum equations and look at the convection terms, pressure gradient terms and the viscous diffusion terms. (2). The friction factor is related to the viscous diffusion terms, and is evaluated at the wall. (3). But I guess, if the contribution from the convection terms is zero for fully developed pipe flow, then the viscous loss will be equal to the pressure gradient term, from the momentum equations. In that case, you can evaluate the viscous loss by calculating the pressure gradient term. This is the case in your friction factor formula. (4). In general, the convection terms are not zero, therefore, you will have to evaluate the friction factor directly from the viscous terms, that is from the skin friction at the wall.

Re: caculation of friction factor
Dilip, It seems to me that you're formula for the average friction factor is correct. Also static pressure should be area averaged as you propose. This procedure should be appropriate even with reversed flow, however, I'd choose my 1 and 2 points so that there is as little as possible.
By definition you should be able to calculate the average friction factors and Nusselt numbers in this way (using a control volume). To check one can of course calculate the local values and integrate over the length on interest. If I recall correctly for the Nusselt number one should calculate the local heat transfer coefficient, find the average value of that and then find the average Nu. Consult an introductory heat transfer book. 
Re: caculation of friction factor
Thanks john for your response. I always appreciate your nice explanation on this forum. I understand that in case of fully developed flow skin friction coefficient calculated from wall shear stress is same with the friction factor calculated from pressure gradient. But for developing flow where the convection part is not zero, the skin friction coefficient is different from the friction factor. In that case, how the friction factor is to be calculated from skin friction?? I think that is calculated from pressure difference only.
Thanking you, dipak 
Re: calculation of friction factor
Thanks for your response. But i couldn't understand, "appropriate even with reversed flow, however, I'd choose my 1 and 2 points so that there is as little as possible."....as little as possible what??
Waiting for your reply. Dilip 
Re: calculation of friction factor
Hello!By the by I would like to get clarified on one the following points: (1)For fully developed flow through pipes the friction coefficient is given by the symbol: f Some authors call it as Darcy's coefficient also.Some others put up a term "Coefficient of friction" and multiply it by 4 to get the friction factor value.Some autors use both the names at will as if they are the same.This is a problem for both teacher and students.Now the question is whether they represent the same term or different? (2)In the formula for finding the specific speed of cenrifugal pumps the value of discharge is substituted in the unit of litres/sec in some books and in cubic metres/sec in some other books.Is it because of the unit system followed or one of the above should not be used? As a teacher of fluid mechanics I have been facing the problem for some time and authentic replies will be of great help.

Re: calculation of friction factor
As little reversed flow as possible.

Re: calculation of friction factor
Hi!
The Darcy (D) friction factor is related to the Fanning (f) friction factor as: D=4f /Esa 
Re: calculation of friction factor
Dilip sorry for not getting back to you sooner. i meant as little reversed flow as possible

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