friction factor and materials

[MrReds]

Hi all !

I am sorry to disturb you with a so banal question, but I'd need your help to clarify a basic doubt.

This doubt is:
if I use f = 0.046/Re^(-0.2)

to calculate the friction factor, this factor is independent by tube material.
This means that if I use this formula, if I have the same flow and the same section, I would obtain same pressure drop in a pipe of plastic, a tube of copper, a tube of iron ecc...
Nevertheless, I am no so convinced of this.
That is: the material of tube influences the pressure drop.
Please, could you explain me what is wrong in my argumentation ?


Thanks a lot

 

[BigInch]

Nothing's wrong.

the exponent -0.2 needs to vary to compensate for pipe roughness.


"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
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[stanier]

There are other expressions for "f" that provide you with the explicit input for diameter, surface roghness etc. Pipe material per se does not come into it however different materials have different diameters and surface roughnesses.

 

[BigInch]

Or I've also found these friction factors,

Laminar flow, f=16/re
commercial pipe, f= 0.054/re^-0.2
smooth tubes, f = 0.046/re^-0.2
Extremely rough pipe, f = 0.013

"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
***************

http://virtualpipeline.spaces.live.com/

 

[stanier]

http://en.wikipedia.org/wiki/Darcy_friction_factor_formulae

This website contains more extensive versions of the Colebrook White method of determining the Darcy friction factor.

 

[katmar]

MrReds, Your equation seems to be a modified version of the Blasius Equation aimed at giving more accurate results at higher Reynolds numbers. BTW in your equation the Reynolds number should have the exponent +0.2 and not -0.2.

The Blasius Equation is
f = 0.0791 / (Re^0.25)
and is recommended for the Reynolds number range 5,000 to 100,000.

This equation (and yours as well) is limited to "smooth" pipes. Unfortunately "smooth" is not an absolute definition. At a Reynolds number of 10,000 any pipe with a e/D ratio of 0.0005 or less could be regarded as smooth, but at Re=100,000 the e/D ratio would have to be less than 0.00005 to qualify as smooth. This is why your equation is independent of the pipe material. It doesn't matter, as long as it is "smooth".

At a Reynolds number of 10,000,000 (i.e. above the recommended limit for Blasius) the Moody diagram would give a friction factor of 0.00205, while your equation gives 0.00183 and Blasius gives 0.00141. This is why I say your equation seems to be aimed at improving estimates at high Re.

At the low Re end your equation is a bit less accurate than the original Blasius.

Note that both equations here are giving the Fanning form of the friction factor, which is 1/4 of the value in the Darcy or Moody form.

If you click on the FAQ link at the top of this forum you will find a very thorough review by Quark of the many friction factor correlations available.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[BigInch]

Katmar, I think those are for the form of F = 1/f

"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
***************

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[vzeos]

I think katmar gave a good explanation (except for the typo 10,000,000.) Most of the early approximations to the smooth pipe law were variations of the Blasius equation. What is F = 1/f? Did you mean F=1/[√]f?....I suspect this is the reason the U. S. Bureau of Mines Monograph No 9 coined the term Transmission Factor for 1/[√]f.

 

[katmar]

@BigInch
The form of the equations I gave is correct. See for example Perry 7th Ed, pg 6-10, Equation 6-37.

@vzeos
Why do you think 10,000,000 is a typo? Unless the confusion is between decimal points and decimal commas. My intention was to convey the number 10 million, or 1.0x10⁷. The upper limit generally given for the Blasius equation is 100,000 (one hundred thousand or 1.0x10⁵) and I was trying to show that the modified equation given by MrReds performed better than Blasius beyond this limit.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[vzeos]

katmar,
You are correct. The typo is in my reading. I read "...the above recommended..." instead of "...above the recommended..."

 

[BigInch]

Yes yes. those "/" should be "*".

Good work Katmar.

"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
***************

http://virtualpipeline.spaces.live.com/