Reference problem
=====================


Geometry
---------


.. image:: images/100008FA0000319C000011C76119886E1226E597.svg
    :width: 480
    :height: 172


.. _RefImage_100008FA0000319C000011C76119886E1226E597.svg:

Circular cross section pipe:

Outside diameter: :math:`0.1m`

Thickness: :math:`3\mathrm{mm}`

The gravity field is not taken into account.


Material properties
-----------------------


.. csv-table::

    "Young's modulus of the pipe:", ":math:`E=2.1E+11N`"
    "Pipe compressibility coefficient:", ":math:`\nu =0.3`"
    "Pipe density:", ":math:`\rho =7800\mathrm{kg}/{m}^{3}`"
    "Fluid density:", ":math:`{\rho }_{f}=8.3\mathrm{kg}/{m}^{3}`"
    "Fluid speed:", ":math:`c=495m/s`"



Boundary conditions and loads
-------------------------------------

Degrees of freedom :math:`\mathrm{dy},\mathrm{dz},\mathrm{drx},\mathrm{dry},\mathrm{drz}` are locked for the entire pipe.

On the acoustic section, DX is also blocked and the only free degrees of freedom are :math:`\mathrm{PRES}` and :math:`\mathrm{PHI}`.

At the end of the tank side: :math:`\mathrm{PRES}=0.` :math:`\mathrm{PHI}=0.`