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authorPaul Garlick <pgarlick@tourbillion-technology.com>2020-07-23 16:03:10 +0100
committerPaul Garlick <pgarlick@tourbillion-technology.com>2020-07-23 16:03:10 +0100
commitaaf0716c398b68d3b88943286cd5e4fd48bcdd92 (patch)
tree2b712d0f634681fece83ace905bf69e7e9259ba5 /doc
parent2ba20ce8e923bfc066244eaf8249a7e8eeaaf547 (diff)
downloadfullSWOF-utils-aaf0716c398b68d3b88943286cd5e4fd48bcdd92.tar.gz
doc: Add theory chapter.
* doc/fullswof-utils.texi (Theory): New chapter.
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diff --git a/doc/fullswof-utils.texi b/doc/fullswof-utils.texi
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--- a/doc/fullswof-utils.texi
+++ b/doc/fullswof-utils.texi
@@ -46,6 +46,7 @@ Utility scripts for the FullSWOF shallow flow solver
@menu
* Installation:: Installing FullSWOF-utils.
* Usage::
+* Theory::
* Demos::
* GNU Free Documentation License:: The license of this manual.
* Index:: Complete Index.
@@ -368,6 +369,74 @@ format.
Quit @command{slope.py}.
@end table
+@node Theory, Demos, Invoking slope.py, Top
+@comment node-name, next, previous, up
+@chapter Theory
+
+The values of discharge and height calculated by the @emph{makeBoundary}
+program are based on a one-dimensional analysis of friction loss in
+channels. The formulae applied are Manning's equation and the
+continuity equation. A summary of the background theory is given in the
+@cite{Fluvial Design Guide}@footnote{See
+@url{http://evidence.environment-agency.gov.uk/FCERM/en/FluvialDesignGuide/Chapter7.aspx?pagenum=4,
+Section 7.4 Fundamental hydraulic principles}.} published by the
+Environment Agency.
+
+In @emph{makeBoundary} the one-dimensional analysis is implemented in a
+series of steps. The first step identifies the number of regions, or
+''panels'', that make up the boundary. The markers at the start and end
+of each panel are listed in the boundary definition file
+(@pxref{Boundary Definition File}). In the next step the minimum and
+maximum heights are established for each panel. The minimum height
+is the height at the bottom of the channel. The maximum height is the
+height at which overtopping starts to occur.
+
+The next step is to generate a @emph{rating curve} for each panel. The
+rating curve relates the discharge @emph{Q} to surface elevation
+@emph{h} for the steady flow condition. The discharge is defined by the
+continuity equation:
+
+@indentedblock
+ @math{Q = A V}
+@end indentedblock
+
+@noindent
+where @emph{A} is the cross-sectional area of the flow and @emph{V} is
+the flow velocity. For the case of channel flow, @emph{V} is given by
+Manning's equation:
+
+@indentedblock
+ @math{V = (1/n) R@sup{2/3} S@sup{1/2}}
+@end indentedblock
+
+@noindent
+where @emph{n} is the Manning coefficient of roughness, @emph{R} is the
+hydraulic radius and @emph{S} is the friction slope. The hydraulic
+radius is the ratio of the cross-sectional area @emph{A} to the wetted
+perimeter of the channel @emph{P}. The friction slope is taken to be
+equal to the slope of the channel bed for the case of steady flow.
+
+It is convenient to introduce the term @emph{conveyance} to directly
+relate the discharge to the slope. The conveyance @emph{K} is given by
+the expression
+
+@indentedblock
+ @math{K = A (1/n) R@sup{2/3}}.
+@end indentedblock
+
+Discharge and slope are then related by the expression
+
+@indentedblock
+ @math{Q = K S@sup{1/2}}.
+@end indentedblock
+
+In order to generate data for the rating curve the conveyance and
+discharge are calculated for a set of water levels within the minimum to
+maximum range. At each level the wetted perimeter and the
+cross-sectional area are calculated. From these values the hydraulic
+radius is calculated, allowing the conveyance to be determined.
+Finally, the discharge is calculated from the conveyance.
+
@node Demos, GNU Free Documentation License, Boundary Definition File, Top
@comment node-name, next, previous, up
@chapter Demos