C.F.Colebrook

Nikuradse had shown the shape of the  versus Re curve during the transition from hydraulically smooth flow to hydraulically rough flow for pipes which had been artificially roughened with graded sand. It now became important to find out the shape of the transition for the sort of surface produced in ordinary commercial pipes because most pipes would work in this transition range.

 

In a real pipe that might be used in engineering the internal surface is produced by one of several manufacturing processes. One might reasonably expect that pipes made by a given process will have more or less the same surface texture regardless of the pipe diameter. We have seen that in any given pipe the flow will change from being hydraulically smooth to hydraulically rough. For commercial pipes made by a given process the value of Re at which the change starts increases as the diameter of the pipe increases. So, if a series of commercial pipes of different diameters but all made by the same process are tested, a family of curves of  versus Re can be plotted. The interest will lie in the shape of the transition from hydraulically smooth to hydraulically rough flow.

 

Colebrook experimented along these lines and presented his work in 1938.[1] In assessing his presentation we should remember his objective, as a scientist, and not try to assess it according to the objectives of engineers. He sought a presentation that would give a universal curve both for his results and those of Nikuradse.

Graph 7-6 shows his plot of  against . The origins of this plot are not relevant to this chapter[2], the important result is that, for commercial pipes the transition from hydraulically smooth to hydraulically rough conditions is a smooth curve. Existing data was added to the Colebrook plot and soon there was ample evidence to confirm this smooth transition and that the shape of the transition was more or less independent of the surface texture of the pipe.

This opened the way for the evolution of the final diagram by Moody.