Pressure drops in elbows 1

[ONEPOINT]

Why the 90 degrees short-radius elbows create a larger pressure drop inside the line, then the 90 degrees long-radius elbows?Could this be illustated by a mathematical equation?

Is there any difference in pressure drops between the 45 degrees elbows and the 90 degrees long-radius elbows?

 

[m777182]

The velocity profile is much more distorted in a short radius elbow.There is more shearing and consequently higher pressure loss.
m777182

 

[Latexman]

Crane TP 410 speaks in some detail about resistance of bends. They mention three components of head loss:

1-the loss due to curvature
2-the excess loss in downstream tangent
3-the loss due to length

I understand 1 and 3. Can someone explain 2?

Good luck,
Latexman

 

[DesignerMike]

I'm sure you research will also show that the pressure loss is proportional to the fluid velocity.

I have one customer that thought they needed long sweep elbows for their high viscosity product, BUT in reality the high viscosity required such a large diameter tube to keep the pressure loss down that our line velocity was so slow (less than .7 fps) it didn't matter.

 

[LHA]

Latexman:
It's been well over a decade since I've had courses in all this, so I'll just rely on memory, and common sense.

It sounds like "downstream tangent" is referring to the point at which the flow regime changes - the bend transitions back into a straight run, or into a diffent degree of curvature. Any transition of fluid flow will introduce turbulence. Turbulence will lead to losses which are independent of other losses.

Does that sound good?

Remember: The Chinese ideogram for “crisis” is comprised of the characters for “danger” and “opportunity.”
-Steve

 

[Latexman]

It could be. I know while the fluid is in the bend(s) it has secondary flow induced by the curvature and frictional flow. This term may account for it changing from that back to the normal axial turbulent flow.

Good luck,
Latexman

 

[rconner]

I believe the “Kshape”, or minor loss coefficient (K or Ks), can be found e.g. for 90 degree ells/bends with various R/D and e/D ratios using Fig. #28 from “Handbook of Applied Hydraulics”; Davis & Sorenson, 3rd Ed. Pg 2-24. I also think these ell/90 values so determined could be multiplied by a correction factor C45 as per Fig. 10.6 of “Fundamentals of Pipe Flow”, by Robert Benedict, pg 371 to find a corresponding value for 45 degree bends. From a purist theoretical standpoint, there will also be additional minor losses at each pipe-to fitting end connections, when there is any difference in the inside diameter of the bend fitting relative to the entry and exiting pipe inside diameters as well (i.e. the expansion and contraction effect at any varying inside diameter “step”).

From a practical point of view, at least with regard to contemporary ductile iron pipe and fittings for water and sewer applications, there is normally very little if not insignificant minor head loss with contemporary bend fittings, at even say a 90 degree ell location, with all this being considered. In testing some time ago at the flow facility at Utah State University, a 24” (~600mm) 90 degree ANSI/AWWA C153/A21.53 (“compact” design) latest configuration ell fitting/pipe assembly with standard cement mortar lining manufactured by ACIPCO was found to have an overall (including expansion and contraction pipe end connection effects) effective minor loss coefficient value slightly less than 0.7. I believe this value, that equates to a headloss of less a tenth of a psi at a flow velocity of 3 ft/sec (~1 m/sec) based on the relationship HL=KsV^2/(2G), may be compared to the following traditional references for prior ell minor head loss coefficients:
1. K Factor .90 Reference “Civil Engineering Reference Manual”, 7th Ed., Michael Lindbergh, Professional Publications, pg 17-12, Table 17.4
2. K Factor .9 Reference “Fluid Mechanics”, 7th Ed., Wylie & Streeter, McGraw Hill. Pg 245, Table 5.3
3. K Factor .9 Reference Water Resources and Environmental Engineering, 3rd Ed., Linsley & Franzini, Mc-Graw Hill, pg. 282, Table 11-2e
4. K Factor .75 Reference Manual of British Water Supply Practice, Institution of Water Engineers, Heffer & Sons Ltd., pg. 147, Table XXVII