On the use of generalized Hamilton?s principle for the derivation of the equation of motion of a pipe conveying fluid

In this paper, first, some pertinent studies are reviewed, undertaken to extend Hamilton?s principle or Lagrange?s equations to open systems, and continua including so-called non-material volumes; then, the corresponding mathematical formulations are reproduced and discussed using a uniform nomenclature. A typical flexible pipe conveying fluid system is considered next, and it is shown that the expression given by McIver for Hamilton?s principle remains valid even in the presence of non-material volumes; the extra term due to the flux of kinetic energy through the control surface in the expression obtained by Casetta and Pesce vanishes.