35 degree bend pressure drop calc

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.

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

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,

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

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

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

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!

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!

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