Abstract: Based on a new incomplete simiarity assumption of the simiarity theory and the structure of the asymmetric passing flows, a generalized power-type velocity distribution formula is proposed for hydraulic smooth region, hydraulic transition rough region and hydraulic rough region wallturbulence. Corresponding to the generalized velocity distribution formula, a skin-friction law is derived. Both the velocity distribution formula and the skin-friction law are compared with the classic Nikuradre experimental data.