What is von Karman equation for fully rough zone in pipe flow?
Ans: At very large Reynolds numbers the friction factor curves corresponding to specified relative roughness curves are nearly horizontal in the Moody diagram, and thus the friction factors are independent of the Reynolds number.
The flow in that region is called fully rough turbulent flow or just fully rough flow because the thickness of the viscous sublayer decreases with increasing Reynolds
number, and it becomes so thin that it is negligibly small compared to the
surface roughness height.
The viscous effects in this case are produced in the main flow primarily by the protruding roughness elements, and the contribution of the viscous sublayer is negligible.
The Colebrook equation in the fully rough zone (Re → ∞) reduces to the von Kármán equation expressed as 1/√f =−2.0 log[(𝜀 /D)/3.7], which is explicit in f.