C. PROBLEM FORMULATION 1. Geometric Relationships Assuming that the volume of the Bourdon changes as deformation occurs, the change in the semi-major axis da is expressed as a function of the change in the semiminor axis db by the equation ab.-(E- K) da= db 2.8 E.a2 - K-b2 The derivation of equation 2.8 is presented in Appendix A. For a unit length, the volume ofthe Bourdon is defined by the equation V=r. a.b 2.9 The change in volume then becomes dV= n (a-db + b-da) 2.10 or dV\-' a(a(2 +_b2)_E - *2Kb2 .db 2.11 Ea2_ Kb2 J by making the substitution for da in equation 2.10. Bourdon tip travel is a function of the sectional deformation that occurs as a result of pressurization. For an applied internal pressure, a curved circular tube will not 18 12.230.
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