On the principle of least action in terms of incompressible fluid flow in a channel of variable cross-section

A formulation of the principle of least action is proposed as applied to the stationary motion of a non-viscous, non-heat-conducting, incompressible fluid in an axisymmetric channel of variable cross section. As a result of solving the variational problem corresponding to this principle, a connection was found between the components of the velocity vector, which made it possible to determine the shape of the channel in which the implementation of the principle of least action is ensured, and the flow parameters both in the channel itself and in the initial outflow region - the region that forms the flow in some conditional section of the entrance to the channel