The article summarizes the results and discusses the application of the method of dimensional analysis to the problem of a real fluid flow past a circular cylinder. It presents the models which take into account the basic laws of kinematics and dynamics of the free fluid flow on the front of the streamlined cylinder, which can be useful both for the qualitative analysis of the phenomenon and for obtaining quantitative estimates. Dependencies characterizing the kinematics and dynamics of the fluid flow to the streamlined cylinder were deduced. The solution of the problem of the flow past an obstacle is of practical importance and can be used, for example, to predict the erosion upstream of intermediate bridge supports, to calculate the forces acting on projections and to design certain types of water intake facilities, etc.