Equivalent lengths/K values for pipe crosses

[LaSalle1940]

Most if not all those who post/read here are familiar with the various compilations of equivalent lengths and K values (either the Crane single K, the Hooper two K, or Darby three K method) for evaluation of pressure drop through pipe and fittings. As such, I'm sure that everyone is aware that tees show up with flow directed either through the run or out the side port. However, those lists seem to ignore crosses uniformly.

My sense is that crosses can be approximated by tees reasonably well for straight-through flow; however, my sense is that flow into/out of adjacent ports could be covered by approximating that situation as two tees of the same size with flow out the side outlet: I say this because that would (in theory) account for the two dead legs thus encountered, and any eddies/turbulence within the fitting.

Has anyone seen a tabulation of K values or equivalent lengths that includes crosses? And if so, what is the source of that tabulation? Thanks.

 

[Mech85]

Section 13.9 of Internal Flow Systems by D.S. Miller (Volume 5 of BHRA Fluid Engineering Services) gives loss coefficients (K) for "4-way dividing junctions with all legs of equal area and sharp edges".

There are two charts - one for through flow and one for branch flow. Hope this helps.