A family of exact solutions of the Navier-Stokes equations for the verification of computer programs

A family of axisymmetric solutions to the Navier-Stokes equations, of linear in rate, is found. Any linear combination of the rate fields of this family is the rate field of some solution to the Navier-Stokes equations, which is included in the found family. Generally speaking, different solutions have different streamline patterns that change with time. Unlike the well-known screw solutions, the nonlinear and viscous terms of the Navier-Stokes equations are not equal to zero. Therefore, the new solutions correspond to nondegenerate Navier-Stokes equations. The obtained exact solutions are proposed for the verification of various approximate methods and software complexes intended for calculating the flows of a viscous incompressible fluid.