An exact solution of a fluid-structure interaction problem

We construct an exact solution for a stationary fluid flow through a channel with upper wall attached to an elastic spring. The position of the upper wall is determined from the interaction between the fluid and the wall. It is displacement computed from a quartic equation that can be solved by radicals and the solution is proved to be physically reasonable.

Automated summary

An exact solution was constructed to describe the stationary fluid flow through a channel with the upper wall attached to an elastic spring. The position of the upper wall is determined by the interaction between the fluid and the wall, with the displacement calculated from a quartic equation that can be solved by radicals and has been proven to be physically reasonable.