New friction factor equations developed for turbulent flows in rough helical tubes

• New friction factor equations for turbulent flows in rough helical tubes are derived.
• Equation parameters are obtained by regression analysis of experimental data.
• Curvature makes the friction factors in rough straight and helical tubes different.

Helical tubes are widely used and there lacks friction factor equations for turbulent flows in rough helical tubes. Turbulent flows in rough helical tubes were investigated theoretically in this paper. Friction factor equations for transitionally and fully rough regime turbulent flows in rough helical tubes were derived based on the logarithmic velocity distribution law. The parameters of the equations were obtained by regression analysis of experimental data of Clancy (1949) and verified by experimental data of McElligott (1948). The characteristics of the friction factors in rough helical tubes were discussed based on the equations. Friction factors of helical tubes are influenced by Reynolds numbers, relative roughnesses and curvature ratios. The friction factors of rough helical tubes can also be divided into a transitionally rough regime and a fully rough regime according to the roughness height and the Reynolds number like that for straight tubes. Roughnesses have greater effects on the transition from the transitionally rough regime to the fully rough regime than that of curvature ratios. Roughness effects on friction factors increase with the increasing of the curvature ratio and the Reynolds number.