Dynamic of axisymmetric stream flowing out of a small round hole
Exact solutions of the equation of the hydrodynamic boundary layer of the incompressible fluid flow for an arbitrary function of the pressure gradient are found. The functions of the current and the distribution of the velocity field in the cylindrical coordinate system are determined. Further, the exact solution of the partial differential equation is sought in a self-similar form and a nonlinear ordinary differential equation of the third order is obtained with respect to an unknown function. The pressure gradients were assumed to be equal f (x) = Ax<sup>k</sup>, where A - is a constant value. At a value of, the equation in question is integrated in quadratures and the resulting solution describes an axisymmetric jet. The solution found by the method of separation of variables and presented in cylindrical variables determines the boundary layer of the stationary flow of a viscous fluid on an extended body of rotation. In the case, the solution of the differential equation is sought in a self-similar form and the solution found at the value of the self-similarity index also determines the axisymmetric jet flowing out of the round hole. The functions of the current, the components of the velocity vector, the pulse flow are determined. a picture of the current lines and velocity profile, the volume of liquid flowing in the jet in one second. The solution of the equation of an asymmetric unsteady boundary layer describing the unsteady flow of an incompressible viscous fluid on an extended body of rotation is found