Effective Length in a tube (intake / exhaust)

[johnnySV]

hello all,

i am having trouble finding the equations necessary to determine the 'effective length' in a bent section of pipe. this is for intake runner / exhaust header purposes.

the concept i am chasing is that 12" of straight pipe does not have the same flow characteristics as a 12" straight section bent to 45degrees. however, that bent 12" section should have an 'equivilant length' equal to a straight pipe longer than 12"

i would imagine this is pretty trivial but i didnt have much luck finding it in my fluids book; and when i google it returns lots about acoustic resonnance in straight sections (for music, etc.)

i have some bendy runners and i would like to determine their effective length. thanks for your help.

[johnnySV]

hello all,

i am having trouble finding the equations necessary to determine the 'effective length' in a bent section of pipe. this is for intake runner / exhaust header purposes.

the concept i am chasing is that 12" of straight pipe does not have the same flow characteristics as a 12" straight section bent to 45degrees. however, that bent 12" section should have an 'equivilant length' equal to a straight pipe longer than 12"

i would imagine this is pretty trivial but i didnt have much luck finding it in my fluids book; and when i google it returns lots about acoustic resonnance in straight sections (for music, etc.)

i have some bendy runners and i would like to determine their effective length. thanks for your help.

[jonnycowboy]

In your fluids book you'll have the bernoulli (or energy) equation. you can use that along with the "K" factors for pipe characteristics (bends, entrances, exits, and valve friction) to determine what the equivalent length will be.

[rjwoods77]

S=axr. Arc length equals angle of bend x radius.

[johnnySV]

johnnycowboy - my fluids book has a general table for K factors... it simply states that a 90degree elbow will have K=0.2 more specifially i am looking for the loss factor (which would hopefully translate to effective length of straight pipe) for 10 degrees worth of a bend in a 1.62" ID tube with centreline bend radius of 2.5"

Rob - i believe the equation you present would be the actual length of pipe used in a bend if the bend were straightened. i thought that the frictional effects of a bent section would be greater than its equal length, straight, counterpart; therefore resulting in a need for an 'effective length' calculation.

am i incorrect to assume this ??
thanks again,

[rjwoods77]

I was working on something awhile ago and came across a book that had more exact stuff on k factors. Go ask a fluids professor. He/she would have something like that.

That was just an arc length equation yes. But you have to start somewhere. The centerline is where you start to "average" everything anyway so it is good to know.

[Charlie]

There is some information about this in Winterbourne and Pearson's book. It is not a simple equation as far as I have found. It's something you must find experimentally. However flow is always biased towards the outside of a bend; it most case studies I've seen a good approximation can be the length of the outside distance averaged with the middle arclength.

[BeaverGuy]

if you want equivalent length for frictional losses, then the relationship is

Leq=k*D/f

where Leq is the equivalent length, K is the fitting or bend loss factor, D is the diameter of the pipe prior to the fitting and f is the friction factor of the pipe before the bend.

For the factor Kb the relationship for bends is:

Kb=(n-1)(0.25*pi*f*r/d+0.5K)+K

where Kb is the K factor of a non-90 degree bend, n is the number of 90 degree bends(so if only a 10 degree bend n would be 1/9), r is the radius of the bend at the centerline, d is the pipe diameter, f is the friction factor of the pipe, and K is the factor for a 90 degree bend dependent on r/d and is given in the table accompanying that equation as
r/d=1 K=20f
r/d=2 K=12f
r/d=3 K=12f
r/d=4 K=14f
r/d=6 K=17f
r/d=8 K=24f
r/d=10 K=30f
r/d=12 K=34f
r/d=14 K=38f
r/d=16 K=42f
r/d=18 K=46f
r/d=20 K=50f

the equation and K factor table is from Technical Paper 410 of the Crane Company.

[johnnySV]

righton.

i think that with Rob's approximation, and BeaverGuy's Leq formula this will give me what im looking for.

my current speedbump comes from the K Facotor table presented by BeaverGuy. my r/d = 1.543, as i see these tabular values have no apparent linear correlation, i dont suppose i could interpolate? i guess i will try to find Technical Paper 410 of the Crane Company to see if the K values are further itemized? if you have an electronic copy of this paper it would be greatly appreciated: jptansey@alumni.unh.edu

thanks,

[BeaverGuy]

I wish I had the whole paper, but only the section of the paper regarding fitting loss equations was given. It was provided as a handout in my thermal/fluid systems design class.

[Ben Beacock]

I'm working out these Leq from beaverguy's formula. for 1-5/8" tubing, 2.5in radius bend I get r/d of 1.658
I couldn't find f, so i used a value of 0.015 to get a K=0.2 at 90deg

but the Leq = 520mm for 85deg of bend or 823mm for 171 deg of bend.

Is this realistic? I don't think I want to add 30cm of runner length to the runner to compensate http://fsae.com/groupee_common/emoticons/icon_confused.gif It would seem the wave harmonics have more association with the air volume than the wall friction.

[John Bucknell]

From a pressure wave tuning aspect, the length is THE length. From a frictional loss point of view, you can use pipe losses. Tuned speed will not change with bends....

[Charlie]

According to Winterbourne and Pearson tuned length does change with bends. The majority of the air follows the OD of the bend and this creates a longer tuned length. This makes good sense to me. I'd love to hear why you disagree.

However this doesn't mean the frictional length formula is going to show you what that difference in tuned length will be. I don't think that is the case either.

[John Bucknell]

Charlie,

You're right - I too often try to generalize to get you going down the right path. Acoustically, intake manifolds almost never tune at exactly the engine speed the model says it should (max error ~10% in the most exotic design) - due to a variety of factors. However the equations used in the above posts are for hydraulic losses, not intended for acoustic purposes at all. So, if you are designing an intake - rough in your tuned length based upon the centerline of the tube. Acoustic pressure waves superposition on top of the local pressure, amplitude hardly affected by the small differences in density caused by 'biasing' caused by flowing around the OD of a bend (ie the difference inside to outside is measured in pascals, not kilopascals).

So yes, your volumetric efficiency may not be as high as you'd like at the tuned speed because of the 360 deg bend you put in your intake pipe.

[Frank]

frictionally speaking...

i dont see all the hoo haa about bent inlet pipes... the restrictor and sudden expansion dominate..

http://www.uq.edu.au/fsae/2004%20Photos/DSC00158.JPG
(acceleration winnner fs2004 fsae-a2004)

[Sam Zimmerman]

The end effects of the pipe dominate any discrepancies between effective length and physical length, and this is true throughout your intake. You should be adding between 0.6 - 1.7 times your diameter to your lengths for end effects. Other factors such as acoustic absorption would introduce more error as well.

The bends can be ignored from an acoustic point of view. If you can get that accurate in your acoustic modeling you are better than I am (which may not be too difficult). http://fsae.com/groupee_common/emoticons/icon_wink.gif

[John Bucknell]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Frank:
frictionally speaking...

i dont see all the hoo haa about bent inlet pipes... the restrictor and sudden expansion dominate..
</div></BLOCKQUOTE>

I was actually talking about runners, which are also intake pipes....

[Frank]

"I was actually talking about runners, which are also intake pipes...."

ditto