% Verbal description for system Weirs (Weirs_desc.tex)
% Generated by MTT on Thu Jul 3 10:27:26 BST 1997.

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% %% $Id$
% %% $Log$
% %% Revision 1.1  2000/12/28 17:47:43  peterg
% %% To RCS
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% Revision 1.1  1997/09/11  10:31:48  peterg
% Initial revision
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   The acausal bond graph of system \textbf{Weirs} is
   displayed in Figure \Ref{Weirs_abg} and its label

%corresponds to flow inertia; but it is admitted that ideal
%\textbf{Sw} components would give a simpler approximation in this
%case. So the modeller has the choice of having a simple simulation
%problem but with four extra states, or a complex simulation with model
%switching but without the four extra states.

The system was simulated for 20 time units and the resultant level of
each tank partition is plotted in Figure \Ref{fig:Weirs_odeso-noargs.ps}. Each
partition has unit cross section, and the two weir heights are $1$ and
$2$ respectively; the inflow $f$ is given by:
\begin{equation}
  f = 
  \begin{cases}
    1 & \text{if $t \le 10$}\\
    0 & \text{if $t > 10$}