==========================================
Air Flow over Cylindar (Under Development)
==========================================

.. py:currentmodule:: solvcon.parcel.bulk

In this chapter we perform the numerical simulations for acoustic field
generated by air flowing over a cylinder.  This problem is chosen to verify the
accuracy of the developed solver.  The acoustic fields are calculated for
different Reynolds numbers

.. math::
  :label: reynolds

  \newcommand{\defeq}{\buildrel{\text{def}}\over{=}}

  \mathrm{Re} \defeq \frac{\rho vD}{\mu}

The density of air is :math:`\rho = 1.2250 \,\mathrm{kg}/\mathrm{m}^3`.  The
dynamic viscosity is :math:`\mu = 1.983\times10^{-5}
\,\mathrm{kg}/\mathrm{(m\cdot s)}`.  Choose the diameter of the cylinder to be
:math:`D = 0.1 \,\mathrm{m}`.  Then, at the three given Reynolds numbers, the
velocity can be calcuated from :eq:`reynolds`:

.. math::

  v = \frac{\mu\mathrm{Re}}{\rho D}

=============== ========= ======== ========
Reynolds number 89,000    46,000   22,000
=============== ========= ======== ========
Velocity (m/s)  14.407102 7.446367 3.561306
=============== ========= ======== ========

.. note::

  In ``examples/bulk/air`` run the following commands to obtain the above
  numbers::

    ./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 89000
    ./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 46000
    ./go velocity --density 1.225 --diameter 0.1 --dvisco 1.983e-5 --reynolds 22000

The bulk modulus of air is :math:`K = 1.42 \times 10^5 \, \mathrm{Pa}`.