Mathematical modeling of hydraulic resistance in pipes with rough walls

Study patterns of flow in pipes with rough walls can be considered relevant, as the use of rough surfaces is a method of heat transfer. In the theoretical study of heat transfer processes in heat exchangers and devices used in various fields of technology, it is very important to know the basic laws of flow in rough pipes in turbulent regime. Flow patterns for rough pipes differs from the behavior for tubes with turbulence, as indicated by both experimental1 and theoretical2,3 studies. Theoretical studies of flow in rough pipes, both experimental and theoretical, are based on the use of a logarithmic velocity profile, which to some extent simplify the mathematical model, which is especially important for large relative (relative to pipe diameter) roughness. Conditions for large roughness can be implemented, for example, in small diameter pipes. It can be compared with the conditions for pipes of small diameters with turbulence.4 Theoretical studies of pipes with rough surfaces are not numerous, sufficiently comprehensive list of studies found, for example, in,5–7 the analysis of which indicates that the theory did not come out of the logarithmic velocity profile. Generated in this study, the theory provides a more complex pattern for the coefficient of hydraulic resistance for rough pipes than existing ones, which provided him with a greater value of validity, a higher accuracy and a wider range of characteristic parameters. It should be noted that more complex patterns have occurred in the study of tubes with turbulence,2–4 which also received a more complex mathematical decision on the coefficient of hydraulic resistance, than those based on a logarithmic velocity profile. Ismagilovich et al.8 discussed the procedure to reduce the hydraulic resistance in turbulent flow comprising to introduce the anti-turbulent admixture to generate Toms effect.