The dynamics of a pipeline conveying one-dimensional unsteady flow is
considered. The dynamics of the fluid-pipe system is represented by a
set of partial differential equations which consists of the axial and
transverse equations of motion of the pipeline and the equations of mo
mentum and continuity of the internal flow. The vibration equations of
the pipeline are derived by use of Newton's law of motion, while the
fluid equations are derived based on the concept of a deformable movin
g control volume. The equations are fully coupled to each other and th
us can be applied to various fluid-pipe interaction problems which can
be generated by the diverse operations of valves and pumps attached t
o the pipeline. The equations are applied to a simply supported inclin
ed straight pipeline to investigate the stabilities and dynamic respon
ses of the pipeline. The stability analysis is conducted by use of Bol
otin's method. The dynamic responses are numerically investigated for
both stable and unstable conditions. It is observed that unstable regi
ons in the stability chart expand as the flow velocity and the mass de
nsity of the fluid increase, and that natural frequencies of the pipel
ine increase as the fluid friction acting on the inner surface of pipe
line increases.