@Pilesar

My question, stated another way, is if *K = f*_{t }* L_{eq}/D and *f*_{t} is defined as the friction factor in a zone of complete turbulence, then how can the K value calculated in this way be applied to any situation other than turbulent flow?

If I were to perform a calculation with my understanding of the article now for a laminar flow situation, it would look something like this:

*h*_{L} = (fL/D + SK) * (v^{2}/2g)

Where *f, L, D* are for the pipe and the K values are for the fittings in the pipe layout. In my equation above, I would have an *f* value for laminar flow applied to the pipe component and K values for the fittings that are defined with a variable that necessitates turbulence (*f*_{t}). This is where I think my confusion with the highlighted portions of the text are applicable - the first portion says the K value may be used regardless of the flow regime while the second portion says turbulence is a requirement. If you read the whole section on page 2, you will see multiple instances of the author emphasizing the turbulent regime as a necessary condition for the applicability of *K = f*_{t }* L_{eq}/D.

I understood the author's intent to separate *f* from *f*_{t} because in the author's view, the head loss through fittings and pipe are different and should be calculated separately, as they detail in the following section and into page 3. Even if you follow the author's prescribed method of performing the calculations, if the flow is in the laminar regime, you end up adding a head loss calculated with a laminar pipe friction factor and a head loss that uses a turbulent flow regime K value for the fittings.

**Edited by jayari, 12 March 2020 - 10:56 AM.**