Model help:BackwaterCalculator: Difference between revisions
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==Model introduction== | ==Model introduction== | ||
The program solves the backwater equation for subcritical flow with a predictor – corrector scheme. | The program solves the backwater equation for subcritical flow with a predictor – corrector scheme. | ||
==Model parameters== | ==Model parameters== | ||
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<headertabs/> | <headertabs/> | ||
==Uses ports== | ==Uses ports== | ||
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|width=50px align="right"|(5) | |width=50px align="right"|(5) | ||
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* Manning-Strickler | * Manning-Strickler formulation | ||
::::{| | ::::{| | ||
|width=500px|<math> C_{f} ^ \left ( {\frac{-1}{2}} \right ) = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) </math> | |width=500px|<math> C_{f} ^ \left ( {\frac{-1}{2}} \right ) = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) </math> | ||
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!Symbol!!Description!!Unit | !Symbol!!Description!!Unit | ||
|- | |- | ||
| | | x | ||
| Streamwise coordinate | | Streamwise coordinate | ||
| m | | m | ||
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| non-dimensional order-one constant | | non-dimensional order-one constant | ||
| - | | - | ||
|- | |- | ||
| H<sub>1</sub> | | H<sub>1</sub> | ||
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|- | |- | ||
| H | | H | ||
| depth | | water depth | ||
| m | | m | ||
|- | |- | ||
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==Notes== | ==Notes== | ||
The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is specified in the input text file. The Manning-Strickler formulation is implemented, when only the coefficients α<sub>r</sub> and n<sub>k</sub> are given in the input file. When all the three parameters are present, the program will ask the user which formulation they would like to use. | The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is specified in the input text file. The Manning-Strickler formulation is implemented, when only the coefficients α<sub>r</sub> and n<sub>k</sub> are given in the input file. When all the three parameters are present, the program will ask the user which formulation they would like to use. | ||
Revision as of 15:55, 11 May 2011
BackwaterCalculator
This program is used for backwater calculations in open channel flow.
Model introduction
The program solves the backwater equation for subcritical flow with a predictor – corrector scheme.
Model parameters
Uses ports
This will be something that the CSDMS facility will add
Provides ports
This will be something that the CSDMS facility will add
Main equations
- Water depth calculation
[math]\displaystyle{ {\frac{dH}{dx}} = {\frac{S - S_{f}}{1 - Fr^2}} }[/math] (1)
- Friction slope
[math]\displaystyle{ S_{f} = C_{f} Fr^2 }[/math] (2)
- Froude number
[math]\displaystyle{ Fr = {\frac{q_{w}}{\sqrt{g H^3}}} }[/math] (3)
- Non-dimensional friction coefficient
[math]\displaystyle{ C_{f} = {\frac{1}{Cz^2}} }[/math] (4)
- Chezy equation
[math]\displaystyle{ Cz = {\frac{K_{Cz}}{\sqrt{g}}} }[/math] (5)
- Manning-Strickler formulation
[math]\displaystyle{ C_{f} ^ \left ( {\frac{-1}{2}} \right ) = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) }[/math] (6)
- Roughness height due to skin friciton
[math]\displaystyle{ k_{s} = n_{k} D_{90} }[/math] (7)
Nomenclature
| Symbol | Description | Unit |
|---|---|---|
| x | Streamwise coordinate | m |
| ΔX | Spatial step length | m |
| S | bed slope | - |
| Sf | friction slope | - |
| Fr | Froude number | - |
| Cf | non-dimensional friction coefficient | - |
| g | acceleration of gravity | m / s2 |
| Cz | non-dimensional Chezy friction coefficient | - |
| Kcz | dimensional Chezy friction coefficient | - |
| αr | user specified parameter | - |
| ks | roughness height due to skin friction | |
| nk | non-dimensional order-one constant | - |
| H1 | starting water depth at the downstream end of the channel | - |
| x1 | starting position | m |
| qw | water discharge per unit width | m2 / s |
| D90 | diameter of the bed surface such that 90% of the distribution is finer | mm |
Output
| Symbol | Description | Unit |
|---|---|---|
| H | water depth | m |
| U | mean flow velocity | m / s |
| η | bed elevation | m |
| Hn | water surface at normal flow | m |
| Hc | critical water depth | m |
| τb | shear stress | - |
| Frn | Froude number at normal flow | - |
| Un | mean flow velocity at normal flow | m / s |
| Uc | critical flow velocity | m / s |
| τbn | bed shear stress at normal flow | N / m2 |
| ξ | water surface elevation | m |
Notes
The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is specified in the input text file. The Manning-Strickler formulation is implemented, when only the coefficients αr and nk are given in the input file. When all the three parameters are present, the program will ask the user which formulation they would like to use.
Examples
An example run with input parameters, BLD files, as well as a figure / movie of the output
Follow the next steps to include images / movies of simulations:
- Upload file: http://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
References
Key papers
Links
Any link, eg. to the model questionnaire, etc.
