35 degree bend pressure drop calc

[joisy]

Hello,

can someone give me the prompting on which formula must be used to calculate the pressure drop through the non-standard angle bend. (assume) I know r/d ratio and angle as well.

"Crane" recommends to use the following formula, but it looks strange:
Kb=(n-1)x(0.25 x Pi x ft x r/d + 0.5K) + K

where n is the number of 90 deg bends, but for eg. 35 deg bend it makes 35/90=0.3889. So, I should substitute this value in place of "n" ???

thanks everyone in advance

 

[25362]

I don't have Crane at hand but I got a list of equivalent lengths of fittings for 90 and 45 degrees elbows, expressed in pipe diameters (based on Crane):

90[sup]o[/sup] std. elbow: 30
45[sup]o[/sup] std. elbow: 16
90[sup]o[/sup] long radius elbow: 20

for street elbows:

90[sup]o[/sup]: 50
45[sup]o[/sup]: 26

For a square corner elbow: 57
For a close pattern return bend: 50

A smaller-than-45[sup]o[/sup] non-standard smooth elbow would have a smaller value than a 45[sup]o[/sup] std. elbow, thus, using the later, one would be on the safe side. True ?

I know the above is not what you expressely wanted. It's only an idea that may result in saving time.

 

[krossview]

Joisy,

I have the Crane Techinical Paper 410-C at hand and can not find the formula you are referring to. In Appendix A-27 the Resistance of bends greater than 90 degrees is based on the formula:

L/D = Rt + (n-1) (Rl + Rb/2)

where:
n = total number of 90° bends in the coil
Rt = total resistance due to one 90° bend, in L/D
Rl = resistance due to lenght of one 90° bend, in L/D
Rb = bend resistance due to one 90° bend, in L/D

Though I can see similarities in the formula, I see no need to derive the formula. The CRANE formula is used to calculate the total equivalent lenght of 2 or more elblows in succesion (ie. elbow+elbow+elbow). As the total pressure loss is less than the sum of the pressure loss for all the 90° elbows.

However, what you try to say or do is this.
If I have an elbow with a 35° bend instead of a 90° bend, can I prorate the pressure loss using the "n" value.

The answer is NO as the formula pertains to a whole number of 90° elbows and not a fraction. Incidently if you plug in n = 35/90 = 0.389 then the first part of you equation becomes negative. Depending on your other variables Kb can be negative too, which is not possible.

Please refer to pages 2-12 and 2-13 of the Crane book and you will see that various investigators demonstrated that the Kb coefficient is actually not that well defined with respect to r/D.

So, what value to use in your case.
I would use an equivalent length for a 45° bend as suggested by 25362 and be done with it.

The answer will be close and it will save you time.

Krossview/OK

 

[joisy]

2 krossview: You are not quite right as the result of L/D = Rt + (n-1) (Rl + Rb/2) will be still positive, but less than Rt. Check yourself.

But it's correct in this case or not? That's the main question!

thanks,

 

[krossview]

Joisy, I should have been more specific in my wording.
You are correct in saying the results of the L/D formula will still be positive and indeed it is less then Rt.
I did a quick table with n = 35/90 and various r/D ratios as per Crane's graph on page A-27.

However, I was actually refering to your original formula and Kb is negative with an r/D = 18, K = 10 and Ft = 1.

I still believe the answer is not correct as the formula applies to more then one bend in succesion and not the fraction of one bend. I am not going to split hairs about finding an exact value as these formula's are based on emperical findings. One can spend a lot of time on this without gaining much value in accuracy.

BTW, can you tell me on what page of the Crane book you found the formula for Kb as I would like to understand the background for this now.
Krossview

 

[TD2K]

Kb is equation 2-20 on page 2-13.

 

[krossview]

Hmm, you guys must have a newer revision then the 1969 issue as page 2-13 does not have equation 2-20. Besides there is no equation 2-20 in chapter 2.

Thanks for your help TD2K

 

[joisy]

You can find this formula in the appendix, section for simple equations to define the resistance' coefficient for valves, fittings, elbows etc. And namely: "Bends"; - with the fittings' pictures!

 

[pleckner]

TO krossview:

I'm not going to claim I have the absolute latest edition but I have the twenty fifth printing, 1991. You really should up date your copy!

 

[joisy]

Assuming that there are no any more ideas on this issue I will put here the formula which looks more or less correct.
(on the base of Crane).

This works for R/D = 1.5 (R - radius of bending, d - diameter of the pipe), e.g. R=1.5D (D - external diameter)

Ang = angle of bend (no less than 30 deg);
St = 90 deg - a constant;
Ratio=Ang/St;
K=(Ratio-1)x(0.25 x Pi x ft x R/d + 7f) + 14f
Where "K" is taken as for 90 deg bend, "f" is a friction factor, d - internal diameter of pipe