10 replies to this topic

[Brightonnk]

Hey everyone, Im doing some work on valve flow coefficients and at the moment am writing a report of my research/calculations. I'm writing about the friction factor and was wondering where the Swamee Jain Equation comes from? is there a derivation of it, if so does anyone know where I can find it or what starting equations I can use to derive it?

Ft = 1/4 (log(e/3.7d)+(5.74/Re^0.9))^-2

Thanks

[breizh]

What about Google?

http://en.wikipedia....factor_formulae

Breizh

[Brightonnk]

Hey I have had a look on google, but I guess what im trying to get at is if theres eqautions where the friction factor equations have been derived from- initially i thought it would have been something to do with:

Friction factor = coefficient of friction x reaction force

But cannot find anything on this?
Thanks

[breizh]

neerakukadia ,

You should try a fluid dynamic text book or Crane TP410M

I've attached a excel sheet , it may help you.


Breizh

Edited by breizh, 31 October 2012 - 01:08 AM.

[katmar]

The friction factor equation that all others are modelled on is the Colebrook equation. The disadvantage of the Colebrook equation is that it has the friction factor on both sides of the equation i.e. it is implicit in f. Swamee-Jain and all the others are simply approximations to the Colebrook equation which allow the new equation to have the friction factor only on the left hand side i.e. they are explicit equations.

There is a good series of articles on this site by Tom Lester explaining how it all fits together. See http://www.cheresour...olebrook1.shtml

[Brightonnk]

Breizh, thanks I have got the Cranes technical paper.
Katmar thanks for the explanation - so the colebrook equation is what I should be looking into. Is there a derviation from first principles of how you get the colebrook equation or is it just a given equation. Im just trying to figure out where all the parameters have come from as it will give me a better understanding in general. Sorry if Im not understanding (still at uni and not completely confident with this topic)

Thanks
Neera

[katmar]

As far as I understand, the Colebrook equation is entirely empirical. It is beyond my comprehension why anybody is still interested in approximations to the Colebrook equation. In the days of slide rules and log tables they made sense, but not any more. If you are using a spreadsheet or writing a subroutine to solve for f, just use Colebrook. It is not that Colebrook is particularly more accurate than any of the others. It is simply the yardstick by which the others are measured, so just go to it directly.

There is a good article on all the different forms of the equations on Wikipedia under the heading "Darcy friction factor formulae". Scroll down to the Goudar-Sonnad equation and consider whether this is really a simplification of the Colebrook equation. For mathematicians having fun it might be an interesting exercise to create an explicit equation. For engineers trying to calculate pressure drops in pipe Colebrook is the answer - and has been for 70+ years.

The only useful work (IMO) is that of Churchill, because he has developed a way to integrate the three flow regimes in a computer friendly manner. But even when I use Churchill's method to combine the flow regimes, I use Colebrook for the turbulent regime.

[Brightonnk]

Perfect, Thanks for all your help. Finally get it!

[breizh]

Neera,
This resource may help you :
http://www.efm.leeds.../pipe_flow2.pdf

Breizh

[S.AHMAD]

Breizh
Very good article. TQ

[Brightonnk]

Breizh
that was a very helpful url - thanks