The formulas for the velocities and resistances in the steady flow of an incompressible viscous fluid in a round cylindrical pipe are analyzed. The law of similarity of velocities in the turbulent regime is used to obtain an explicit representation of the drag coefficient. The relationship between the Reynolds numbers calculated by the average and dynamic speeds is considered. The principle of finding velocity profiles according to the law of resistance is formulated. Analytical expressions are given for the for any flow regime and a formula for taking into account deviations from the logarithm on the velocity profile in the region near the pipe axis.