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but I was hoping to obtain a first principles formula that could equate these losses solely to area and velocity change

The reason being is I am assuming that major losses component of the K values must be based on particular viscosity fluid but I would like to calculate this for different viscosity fluids ?

Also for the Darcy Weisbach if I want to calculate just the frictional losses would I use the average diameter of a convergent or divergent section of pipe ?

If such a formula exists it ok to just plain add these two effects ?

Am I making life to difficult for myself is there an easier way ?