For this specific application, the loading force, F, is the drag force, Fdrag. Since
drag force is a function of tube length, Equation 2.25 is further expanded using Equations
2.1 and 2.3 to obtain Equation 2.26.
Lw pr2 (2.26)
SpV2
Equation 2.26 now shows the wrinkle length as a function of the core contributing
variables for this application; internal pressure, tube radius, and external fluid velocity.
The wrinkle lengths in Equations 2.25 and 2.26 also depend on the boundary conditions
and are derived for the simply-supported conditions shown in Figure 2.4.
2.4 Conclusion
The equations derived in this chapter provide a theory for an inflated beam subject to
bending. The solution for vertical deflection, Equation 2.19, is used to verify the finite
element model developed in Chapters 4 and 5. The wrinkle length is used to verify the
final results of a verification model. Verifying a simple model is necessary to justify
extending the computer analysis to more complex geometries, not easily solved with
traditional analysis.