The Non-linear Equations of Motion of Pipes Conveying Fluid

The non-linear equations of motion of pipes conveying fluid are derived in simple and accessible terms, by energy and Newtonian methods. Different derivations are made for cantilevered pipes, where the centreline is assumed inextensible, and for pipes with both ends fixed; it is shown that the derivations, the origin of the various terms and the structure of the equations are distinctly different in these two cases. The equations of motion are then compared with those already in existence, e.g., by Holmes, Rousselet and Herrmann, and Lundgren, Sethna and Bajaj, at the same time clarifying the derivations and assumptions made, and discussing the validity and completeness of the final equations. Some of the equations are found to be fully correct, indeed superior to those derived here, while others are found to be deficient, because of assumptions made or inconsistencies in the derivations; for pipes with both ends fixed, the equations given in this paper are considered to be the most complete and correct.