Hydrostatic fluid elements are well suited for calculating fluid volume and pressure for coupled problems involving fluid-solid interaction. Modeling with a hydrostatic fluid allows one to study the changes in fluid behavior when it is contained within a solid upon which various loads are imposed.

Such an analysis is useful in the example problem presented here, where it is possible to examine the changing pressure, density and volume of the air inside of a tire during inflation and rolling. Another example application involves the volume and pressure changes of a fluid contained within a cylinder in which a piston is moving.

The automobile industry strives to improve fuel economy and to lessen power loss, both of which are affected by the rolling resistance of a vehicle's tires. To do so, it is necessary to accurately predict the changing fluid conditions within a rolling, deformed tire.