The problem is described in spherical coordinates  with velocity components . The flow is axisymmetric, i.e., independent of . Then the continuity equation and the incompressible Navier–Stokes equations reduce to
where
A self-similar description is available for the solution in the following form,
Substituting the above self-similar form into the governing equations and using the boundary conditions  at infinity, one finds the form for pressure as
where  is a constant. Using this pressure, we find  again from the momentum equation,
Replacing  by  as independent variable, the velocities become
(for brevity, the same symbol is used for  and  even though they are functionally the same, but takes different numerical values) and the equation becomes
After two integrations, the equation reduces to
where  and  are constants of integration. The above equation is a Riccati equation. After some calculation, the general solution can be shown to be
where  are constants. The physically relevant solution to the jet corresponds to the case  (Equivalently, we say that , so that the solution is free from singularities on the axis of symmetry, except at the origin). Therefore,
The function  is related to the stream function as , thus contours of  for different values of  provides the streamlines. The constant  describes the force at the origin acting in the direction of the jet (this force is equal to the rate of momentum transfer across any sphere around the origin plus the force in the jet direction exerted by the sphere due to pressure and viscous forces), the exact relation between the force and the constant is given by
The solution describes a jet of fluid moving away from the origin rapidly and entraining the slowly moving fluid outside of the jet. The edge of the jet can be defined as the location where the streamlines are at minimum distance from the axis, i.e., the edge is given by
Therefore, the force can be expressed alternatively using this semi-angle of the conical-boundary of the jet,