Recent Developments in Fluid Flow through Pipes and Channels and a New Method of Approach for Rough Turbulent Flow through Pipes

Depending upon the Reynold’s Number Nr, a pipe of given relative roughness ro/k may have any of the five zones of flow> viz. laminar, transition from laminar to turbulent, smooth turbulent, transition from smooth turbulent to rough turbulent arid rough turbulent flow. The friction flow equations as given by Prandtl and Karman for smooth and artificially roughened pipes based on Nikuradse’s experiments as also the transition equation for commercial pipes as given by White and Colebrook are discussed at length in this paper. Attempt has also been made to extend the Prandtl’s rough pipe equations to flow through rough channels as well, and the various limitations under which this is possible have been pointed out. Using Prandtl’s rough turbulent equations as bads, the following simple relations have been obtained for flow through rough pipes and channels viz. 1/f = 34.5 (R/K)^1/3 giving Chezy’s C = 47.0 (R/K)^1/6 and Manning’s N ≠ 0.0315. k^1/6. It has further been shown that the above relations are true for values of (R/K) ≥ 4, a limitation which in the opinion of the author has not been pointed out by any other writer before. Also using the abjve relations, a new formula for the design of pipes when the flow is rough turbulent has been developed. This formula is as urder: d^16/3 = Q²L.k^1/3/27 hf The advantage of this formula is that when the given elements of flow are hf, Q (or V), L, ρ, μ, k, the diameter of the pipe can be obtained directly, a problem which till now could be solved only by trial and error method.