  We derive a reduced-order model describing the inflation and deflation
dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar
flow and the extensional motion of the balloon. We initially study the flow and
pressure fields for dictated motion of the solid, which throughout deflation
are obtained by solving the potential problem. However, during inflation, flow
separation creates a jet within the balloon, requiring a different approach.
The analyses of both flow regimes lead to a simple piecewise model, describing
the fluidic pressure during inflation and deflation, which is then verified by
finite element computations. We then use a variational approach to derive the
equation governing the balloon's dynamics, yielding a nonlinear hybrid
oscillator equation, describing the interaction between the extensional mode of
the balloon, and the entrapped fluid. Analytical and graphical investigations
of the suggested model are presented, shedding light on its static and dynamic
behaviour under different operating conditions. Our suggested model and its
underlying assumptions are verified utilizing a fully coupled finite element
scheme, showing excellent agreement.
