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diff --git a/doc/fullswof-utils.texi b/doc/fullswof-utils.texi index 8145934..03e5e9d 100644 --- 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 |