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# Darcy Friction Factor of Stainless OD Tubing ?

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## Darcy Friction Factor of Stainless OD Tubing ?

(OP)
I work mostly with sanitary (ASTM A270) stainless steel OD tubing and in many cases need to model process systems to calculate pressure drops including frictional losses.

In my case the inner surface will either be 32Ra or 20Ra. Does anyone know how, if at all, this can be related to absolute roughness and thus the relative roughness to determine the friction factor (using the Moody Diagram)? I'm using the definition of absolute roughness found in Crane Technical Paper #410 (and many other places I'm sure)...

#### Quote:

(epsilon) = absolute roughness or effective height of pipe wall irregularities, in feet.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

The average roughness can be considered as absolute roughness. For example, 32Ra (I believe it is 32 microinch) has an absolute roughness of 32 microinch. If you are using 50OD tubing then the ID will be about 48mm or 1.8897 inches. So the relative roughness is 32/(1000000*1.8897) = 0.0000169.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

I don't know what a Ra is; I prefer to use engineering units and I've never seen roughness measured in engineering calculations as anything else except mm and inches.  I hate multiple zeros and mm makes for a better positive number.  Plus I like to stick only to those units found in my Uconeer.

I use the same as other engineers I've known: 0.0015 mm for Brass, Stainless Steel, drawn copper, glass,  & plastic pipe.  If there is anyone who has consistantly measured a more accurate roughness height on Stainless Steel tubing, I would like to know who, when, how, and where.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

The industry standards are generally moving toward RA.

ASME B14.6
Roughness average,’ Ra: the arithmetic average of the absolute values of the profile height deviations recorded within the evaluation length and measured from the mean line.  Roughness average is also known as centerline arithmetic average AA) and centerline average (CLA).  The root mean square(RMS) deviation of the assessed profile is Rq.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

The term Ra is used in several industries that deal with sanitary piping/tubing and fittings (bio-phamrmaceutical; Dairy, other food, etc.). The interior of the tubing is super polished either mechanically or electronically to make it super smooth. The object is to eliminate all crevices and the potential for anything to stick/cling to the inside of the pipe that could either contaminate the next product coming down or enhance microb growth. The smoother the pipe the easier it will be to clean with a Clean-in-Place (CIP) system and of course, the more expensive the tubing will be.

I will typically use the roughness factor from Crane TP410 for Drawn Tubing. This hasn't bit me in the bottom yet.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

(OP)
Thanks guys.

Montemayor:
Ra (Roughness Average) is not really a unit, when we say Ra we are referring to a specific measurement/mathematical formula who's units are in microinches (so we are being lazy and not saying microinches). In the food processing, dairy, pharmaceutical and bio-pharm industries Ra is a common specification for surface finish of stainless tubing. This is a standard in the US, and I believe in other countries as well.

Quark:
I'd like to take your word for it regarding the absolute roughness and Ra equivalency (can anyone else verify this?). It does sound logical and that was more or less the answer I was hoping to get. However, like Montemayor I have used a similar value for abs. roughness of .000005 feet (this is pretty close to .0015mm) in the past, which happens to correspond to the 'Drawn Tubing' plot on TP410 pg. A-23. I have always wondered about the accuracy of this though and that was really the point of my question.

Working with the numbers that each of you provided we have:
? ~ 1.4 x 10^-6 feet (Quark)
? ~ 4.9 x 10^-6 feet (Montemayor)

I'm working in feet to keep consistent with TP410 and the moody diagrams therein. Looking at these numbers and their corresponding relative roughness (?/D) there is not a significant difference in friction factors until we get into Reynolds numbers at 10^7 or above, which I personally don't encounter often.

Maybe this has turned into another exercise in academics after all. Anyone else want to weigh in here?

### RE: Darcy Friction Factor of Stainless OD Tubing ?

(OP)
I started my reply and picked up the phone for a few minutes, looks like JL and Pleckner beat me back :)

As mentioned above I have also used drawn tubing and not had any problems, if anything it's probably a little conservative.

In my absolute roughness numbers above I tried to insert the symbol for epsilon, but the forum doesn't play nice with greek letters apparently so we get "?" instead. Anyway you guys get the idea.

I'll probably stick with abs. roughness of .000005 feet, but I'm still curious if anyone agrees with Quark's statement equating Ra and abs. roughness. (Not trying to single you out buddy, just looking for a second opinion

### RE: Darcy Friction Factor of Stainless OD Tubing ?

My 2 cents,

Ra is the average roughness "The average height of the bumps on a surface, measured in micrometres or microinches".

From this to get the absolute roughness (to be used in the Colebrook-White expression) you simply have to calculate Ra/ID where Ra and ID have to be espressed with the same units (meter, micrometer, inches.... so on). In fact to be absolute, dimensionless, the units must be the same :) .

When you get the absolute roughness you can use the Moody's Diagram or better calculate the friction factor using the Colebrook-White expression.

Fred

### RE: Darcy Friction Factor of Stainless OD Tubing ?

I do not have a definitive answer to this, but here are my musings on a very interesting question.

As JLSeagull pointed out, Ra is the average deviation from the mean line. I believe this definition is important in trying to compare this form of specification with the way we usually define pipe roughness.

The diagrams shown at
http://www.edstrom.com/Resources.cfm?doc_id=147 show that for a 32Ra finish the distance between the tops of the crests and the bottoms of the troughs is about 120 micro inch.

In the original work done on pipe roughness by Nikuradse etc they artificially roughened the pipe by glueing a layer of uniformly sized sand particles to the inner surface of the pipe. So what we call the pipe roughness is actually the size of the equivalent sand particles that were used.

Now, seeing that the deviation between the peaks and valleys is about 3.75x the Ra value perhaps we can compare a 32 Ra pipe with one that has 120 micro inch sand particles glued into it.  32 µ" is about 0.00081 mm and if we multiply that by 3.75 we get 0.003 mm.  This compares with the 0.0015 mm that is normally used for drawn tubing.

I have no idea how in reality the smoothness of drawn tubing compares with 32 Ra polished tubing, but as 777gne has pointed out it does not make too much difference to the eventual friction factor in normal applications. Does anyone have an Ra spec for drawn tubing? If I was faced with this problem myself I would probably go with the slightly conservative value of 0.003 mm for the absolute roughness.

To Mr. Montemayor : Before today I had no idea what Ra was either, but µ" is in Uconeer!

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

### RE: Darcy Friction Factor of Stainless OD Tubing ?

(OP)
G4uss:

Did you mean that Ra/ID = relative roughness, not absolute? If so, then it sounds like you're taking the same stance as Quark (see his post above).

I think the answer to this one lies in the definition of Roughness Average and Absolute Roughness (the latter of which will lead us to the relative roughness), and I found the information that katmar presented very interesting.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

#### Quote (777gne):

Not trying to single you out buddy, just looking for a second opinion

In that case, here is the second opinion and I will agree with myself

The quintessential question, as usual, is how many significant digits? Run some calculations with 1.5m/s velocity for various pipe sizes and the difference is from the 3rd or 4th significant digit. But I know that is not the straigh answer, anyhow.

My idea goes like this. The ratio of maximum roughness to Ra depends upon the profilometer probe traverse between sample point to sample point. For example, if there is a peak of 2 mm and then a trough of 2 mm, and the traverse between two sample points is half the slope, then the profilometer reads as 1,2,1 and 2. The average of 4 readings is 1.5 and the maximum is 4(close to the ratio given by katmar). More precisely, the equation is Rmax = 4Ra. Unlike the sand particle method, where the Rmax is the diameter of the sand particle, here it is radius. However, I am not sure whether the trough produces equal friction to fluid flow as that of a peak.

The pipes I use have an Ra value of 0.4 - 0.6 micron (240 grit electropolished) and even if I consider Rmax = 4Ra, the value doesn't come anything nearer to the standard values given above. This has been my practice since 10 years and I am justified for the extra value I pay for electropolishing

### RE: Darcy Friction Factor of Stainless OD Tubing ?

Quark,

#### Quote (quark):

The quintessential question, as usual, is how many significant digits? Run some calculations with 1.5m/s velocity for various pipe sizes and the difference is from the 3rd or 4th significant digit. But I know that is not the straight answer, anyhow.

It may not be the answer to the question, but it is the solution to the problem! Engineering design is a decision and not a calculation. Calculations aid us in our decisions, but at the end of the day the engineer has to decide (for example) whether to use a 3" or a 4" pipe. So I agree with your approach 100%.

I think that the value of your 4 Ra pipe is in the cleanliness rather than in any energy saving due to less friction.

It seems that Prof. Fred Farshad is "the man" when it comes to roughness of pipes. I dug out a few references to articles he has written and hopefully in the next few days I will get a chance to go down to the university library and dig them up. If I have any luck I will let you know.

regards
Harvey

### RE: Darcy Friction Factor of Stainless OD Tubing ?

(OP)
It's been an interesting discussion anyway.

Quark, that's some highly polished stuff you're dealing with. I'd hate to see what it costs! Oh, Katmar, you're correct the reason for using this stuff is not to reduce the friction for energy savings, it is entirely for sanitary reasons.

### RE: Darcy Friction Factor of Stainless OD Tubing ?

A bit off topic.

#### Quote (katmar):

I think that the value of your 4 Ra pipe is in the cleanliness rather than in any energy saving due to less friction.

You are quite right. The basic idea is to avoid formation of biofilms and that size I am speaking about just contains a single bacterial which can be removed easily.

However, had we discussed this topic 5 years back I could have convinced you with whatever logic available in the world. Why? I have seen engineers, here, counting water droplets when they were proposing to change to mechanical seals from gland ropes. Now it is a fixed increment system and salary levels are comfortable.

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