In the paper, the difference between the fractal geometry and the Euclidean geometry,as well as the theoretical basis and calculation formulas of the fractal geometry were briefly introduced.Based on the previous theoretical and experimental achievements for hydraulic resistance laws, the effects of equivalent roughness ks which is used to calculate friction losses of turbulent flow was analyzed.For the application of circular pipe's roughness, mathematical model for fractal dimension was developed based on analysis for fractal characteristics of roughness on pipe's inner wall by using the fractal geometry theory.The relationship between the fractal dimension and equivalent roughness ks was investigated as well and which could provide a direct way for calculating friction losses in the model.The previous theoretical and experimental achievements on resistance laws as well as the model developed in this study could be applied to engineering directly in many practices.