INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS
Log In
Come Join Us!
Are you an
Engineering professional?
Join Eng-Tips Forums!
- Talk With Other Members
- Be Notified Of Responses
To Your Posts
- Keyword Search
- One-Click Access To Your
Favorite Forums
- Automated Signatures
On Your Posts
- Best Of All, It's Free!
- Students Click Here
*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.
Posting Guidelines
Promoting, selling, recruiting, coursework and thesis posting is forbidden. Students Click Here
|
Pipelines, Piping and Fluid Mechanics engineering FAQ
Flow in Pipe
|
Friction Factor Expressions - Implicit and Explicit by quark
Posted: 20 Apr 06 (Edited 31 Jul 09)
|
Friction factor is calculated, generally, by any one of the three implicit equations of Colebrook. The equation, I use, is of the form
1/(f)1/2 = -2.0log((e/D)/3.7 + 2.51/Re(f)1/2)
Note: This is applicable for Re>3000. For laminar flows, Re<2100, Poiseuille's law (f = 64/Re)is used
Engineers, who think that it is difficult to solve this equation, use Moody's chart to get values of 'f'. But, if you go through next FAQ(Spreadsheet for Friction Factors), you will find out how easy it is to solve the implicit equation by some simple calculations in Excel.
To make our life easier, some great engineers developed explicit expressions for the friction factor. As I went on reading the subject, I came to know that there were many explicit expressions that equal no. of hairs on my head (no, I am not bald FYI). Out of those, the following are the famous equations.
Serghides Equation (for Re>2100 and any e/D)
f = [A – [(B-A)2/(C-2B+A)]]-2
A = -2.0 log((e/D)/3.7 + 12/Re)
B = -2.0 log((e/D)/3.7 + 2.51A/Re)
C = -2.0 log((e/D)/3.7 + 2.51B/Re)
Moody Equation (4000<Re<107 and e/D <0.01)
f = 5.5x10-3(1+ (2x104e/D + 106/Re)1/3)
Wood Equation (Re>4000 and any e/D)
f = 0.094(e/D)0.225 + 0.53(e/D) + 88(e/D)0.44 x Rea
a = -1.62(e/D)0.134
Jain Equation (for 5000<Re<107 and 0.00004<e/D<0.05)
1/f1/2 = 1.14 – 2.0 log (e/D + 21.25/Re0.9)
Churchill Equation (for all values of Re and e/D)
f = 8((8/Re)12 + 1/(A+B)1.5)1/12
A = (-2.457ln((7/Re)0.9 + 0.27e/D))16
B = (37530/Re)16
Chen Equation (for all values of Re and e/D)
1/(f)1/2 = -2.0log((e/D)/3.7065 – 5.0452A/Re)
A = log((e/D)1.1098/2.8257 + (5.8506/Re0.8981))
Zigrang and Sylvester Equation (for 4000<Re<108 and 0.00004<e/D<0.05)
1/(f)1/2 = -2.0log ((e/D)/3.7 – 5.02A/Re)
A = log[(e/D)/3.7 – (5.02/Re)log((e/D)/3.7 + 13/Re)]
Comments
After my discussion with Art Montemayor and Katmar, I would dare putting the following comments for member perusal.
1. The friction factor 'f' is Darcy's friction factor(thanks to katmar for pointing out)
2. The comparison of accuracies of these equations is done based upon the presumption that Colebrook's equation is perfect and flawless.
3. Serghides opines that Zigrang equation and his own equation have the higher accuracies (and this is tested by Art Montemayor, Katmar and myself)
4. Away from the critical region, the inaccuracy of any of the above equations is insignificant (as observed by Katmar). I easily accepted this observation due to two facts. The first one is that, the easily available pipes have diameters in steps(i.e if our flowrate requires a pipe just bigger in size than a 3" pipe, our option is 4") . Second one is that, we engineers generally require generous FOS for future expansion and other kind of things.
5. Member Katmar developed a brilliant expression for friction factor by modifying Chruchill's equation, which is in perfect agreement with Serghides and Zigrang as far as accuracies are concerned.
6. Within the critical region, where 2100<Re<3000, one should dare to take the responsibility of calculating friction factor oneself.
7. Katmar opines that Churchill Equation (and so his version of Churchill equation, obviously) is the better one to use for all conditions as it gives a continuous curve when the data is represented graphically. This seems to be a strong point to me.
8. As pointed out by Katmar, one should be careful while using any of these equation for laminar flow or the critical zone. So, instead of using Chen equation for laminar flows, better go with Poiseuille.
9. Please note that Zigrang's equation in Serghides paper is misquoted(first pointed out by TD2K and then I checked it from Zigrang's original paper)
10. Please inform me incase of any mistakes, misinterpretations and misconduct as far as this FAQ is concerned. |
Back to Pipelines, Piping and Fluid Mechanics engineering FAQ Index
Back to Pipelines, Piping and Fluid Mechanics engineering Forum
|
|
Resources
With all of the hype around 3D printing, it can be easy to get lost in fascinating, intricate metal parts made with additive manufacturing. These parts, while impressive, are probably dissimilar from many of the parts you currently produce or use. So why invest in metal additive manufacturing? Download NowConstruction was at one time a highly regionalized business. Pragmatic and market forces made it more efficient for even a large, industrial general contractor to focus regionally. But inexorable trends are making it more important for major commercial, civil, engineering and industrial contractors to grow their global footprint.
Download NowMining is a relatively straightforward business model, driven by cyclical patterns of commodity demand and availability. Disruptive technologies, however, are now offering new tools to teams that enable them to change the rules of the game in their favor. Download NowSelecting business software for a medium to enterprise-sized construction concern is extremely challenging in large part because most enterprise resource planning (ERP) suites originated in the world of repetitive manufacturing and are therefore a poor fit for a project and asset-centric business. However, midsize to large contractors need the predictable, auditable processes that ERP delivers.
Download Now
|
|
Talk To Other Members
