An analytical model of a dynamic boundary layer on a surface in a laminar flow regime

To solve the problems of designing systems operating in Newtonian media in the mode of surface flow, it is necessary to know the characteristics of the motion of media on the flow surfaces. This will make it possible to calculate the energy losses for the transportation of media and the force characteristics of the movement of objects in such media. This paper presents an analytical model of tangential stresses generated on the flow surfaces in a dynamic laminar boundary layer. The flow medium is assumed to be Newtonian. For the universality of the results, the velocity modeling in terms of the thickness of the laminar boundary layer and tangential stresses on the flow surface is carried out in relative parameters. The ratio of the boundary layer thickness y/δ is taken in the range of ≈0...1, the ratio of velocities at the boundary and in the boundary layer is vx /vo = 0...1, and the Mach number is 0.0001...0.1 for a laminar boundary layer. The velocity distribution over the boundary layer thickness and tangential stresses were obtained. The nature of the change in tangential stresses along the boundary layer thickness from ≈0 to 20-10-21 is linear and depends on the Mach number. The tangential stresses directly on the flow surface vary from 704.4 EPa to 704.4 PPa at Mach numbers from 0.1 to 0.0001. The developed analytical dependences of the velocity and tangential stresses allow us to model the dynamic characteristics of the laminar boundary layer on the flow surface for Newtonian media.