Well, the head loss coefficient is only an approximation.
Normally the validity is specified by assuming fully developed turbulent flow. Hence you cannot use them for low Reynolds numbers (e.g. low speed compared to diameter). So indirectly the diameter determines if the approximation is applicable
Another approximation is that they neglect surface roughness. Normally it is assumed that the surface roughness correction for the straight part is sufficient an no additional correction for the bends has to be used.