I have tried Idelchik's Handbook of Hydraulic Resistance 4th Edition (2007 page 300) formulas and across some range the formulas are reported valid for, the law of conservation of energy is violated (expansion loss without kinetic exit loss included) and differs from CFD results, underestimating by order of magnitude of about 137 times (while it agrees in other sub-ranges for which it is reported valid within 3% of CFD results).

I have also tried Ekert et al (1976 pages 30 and 36) on NASA's site: https://ntrs.nasa.gov/api/citations/19770005050/downloads/19770005050.pdf

The results in Eckerts also overestimates by as much as 62% of the CFD results when the diffuser cone angle is 5 degrees whereas it agrees within 7% of the CFD results when the cone angle is 1 degree.

Diffuser Loss formulas which agrees within 5% of CFD results for the range it is reported valid for will be appreciated.

The Friction Loss formulas work perfect but the problem is the accuracy of the expansion loss formulas. I need the formulas to run numerical optimization before generating a geometry for CFD so important I get the analytical/numerical formulas .

Thanks in anticipation of the help