Model help:BackwaterCalculator: Difference between revisions

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1) Log in to the wiki
1) Log in to the wiki
2) Create a new page for each model, by using the following URL:
2) Create a new page for each model, by using the following URL:
   * http://csdms.colorado.edu/wiki/Model help:<modelname>
   * https://csdms.colorado.edu/wiki/Model help:<modelname>
   * Replace <modelname> with the name of a model
   * Replace <modelname> with the name of a model
3) Than follow the link "edit this page"
3) Than follow the link "edit this page"
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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==
= Input Files and Directories =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
|-
!Parameter!!Description!!Unit
|-valign="top"
|width="20%"|Input directory
|width="60%"|path to input files
|width="20%"|
|-
|Site prefix
|Site prefix for Input/Output files
|
|-
|Case prefix
|Case prefix for Input/Output files
|
|-
|}


==Model parameters==
= Run Options =
= First tab header =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
|-
|-
!Parameter!!Description!!Unit
!Parameter!!Description!!Unit
|-valign="top"
|-valign="top"
|width="20%"|<span class="remove_this_tag">First parameter</span>
|width="20%"|Chezy or Manning, Chezy-1 or Manning-2
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"|
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"| -
|-
|}
|}


= Second tab header =
= Run Parameters =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
|-
|-
!Parameter!!Description!!Unit
!Parameter!!Description!!Unit
|-valign="top"
|-valign="top"
|width="20%"|<span class="remove_this_tag">First parameter</span>
|width="20%"|D90 of the surface
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"|
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"| mm
|-
|hydraulic radius
|
| m
|-
|Chezy coefficient
|
| -
|-
|initial depth
|
| mm
|-
|Mean diameter
|
| mm
|-
|alpha (r)
|
| -
|-
|roughness coefficient
|
|
|-
|starting point
|
| m
|-
|Slope
|
| m / m
|-
|water discharge
|
| m<sup>2</sup> / s
|-
|step size
|
| m
|-
|}
|}


= Etc. tab header =
= About =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
|-
!Parameter!!Description!!Unit
|-valign="top"
|width="20%"|Model name
|width="60%"|name of the model
|width="20%"| -
|-
|Author name
|name of the model author
| -
|-
|}
<headertabs/>
<headertabs/>
</div>


==Uses ports==
==Uses ports==
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|width=50px align="right"|(5)
|width=50px align="right"|(5)
|}
|}
* 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
| x
| Streamwise coordinate
| Streamwise coordinate
| m
| L
|-
|-
| ΔX
| ΔX
| Spatial step length
| Spatial step length
| m
| L
|-
|-
| S
| S
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| g
| g
| acceleration of gravity
| acceleration of gravity
| m / s<sup>2</sup>
| L / T<sup>2</sup>
|-  
|-  
| C<sub>z</sub>
| C<sub>z</sub>
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| k<sub>s</sub>
| k<sub>s</sub>
| roughness height due to skin friction
| roughness height due to skin friction
|  
| L
|-
|-
| n<sub>k</sub>
| n<sub>k</sub>
| non-dimensional order-one constant
| non-dimensional order-one constant
| -
| -
|-
| D<sub>90</sub>
|
|
|-
|-
| H<sub>1</sub>
| H<sub>1</sub>
| starting water depth at the downstream end of the channel
| starting water depth at the downstream end of the channel
| -
| L
|-
|-
| x<sub>1</sub>
| x<sub>1</sub>
| starting position
| starting position
| m
| L
|-
|-
| q<sub>w</sub>
| q<sub>w</sub>
| water discharge per unit width
| water discharge per unit width
| m<sup>2</sup> / s
| L<sup>2</sup> / T
|-
|-
| D<sub>90</sub>
| D<sub>90</sub>
| diameter of the bed surface such that 90% of the distribution is finer
| diameter of the bed surface such that 90% of the distribution is finer
| mm
| L
|-
| C<sub>f</sub>
| Non-dimensional friction coefficient
| -
|-
|-
|}
|}
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|-
|-
| H
| H
| depth
| water depth
| m
| L
|-
|-
| U
| U
| mean flow velocity
| mean flow velocity
| m / s
| L / T
|-
|-
| η
| η
| bed elevation
| bed elevation
| m
| L
|-
|-
| H<sub>n</sub>
| H<sub>n</sub>
| water surface at normal flow
| water surface at normal flow
| m
| L
|-
|-
| H<sub>c</sub>
| H<sub>c</sub>
| critical water depth
| critical water depth
| m
| L
|-
|-
| τ<sub>b</sub>
| τ<sub>b</sub>
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| U<sub>n</sub>
| U<sub>n</sub>
| mean flow velocity at normal flow
| mean flow velocity at normal flow
| m / s
| L / T
|-
|-
| U<sub>c</sub>
| U<sub>c</sub>
| critical flow velocity
| critical flow velocity
| m / s
| L / T
|-
|-
| τ<sub>bn</sub>
| τ<sub>bn</sub>
| bed shear stress at normal flow
| bed shear stress at normal flow
| N / m<sup>2</sup>
| -
|-
|-
| ξ
| ξ
| water surface elevation
| water surface elevation
| m
| L
|-
|-
|}
|}
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==Notes==
==Notes==
* Note on equations
The model uses equation 1 to compute the water depth, H, everywhere in the channel for a given water discharge per unit channel width, q<sub>w</sub>, and downstream boundary condition, i.e. a user specified water depth.
The bed slope, S, is assumed constant in the streamwise direction, the friction slope, S<sub>f</sub>, and the Froude number, Fr, are defined as equation 2,3.
* Note on model running
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.


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<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
* <span class="remove_this_tag">Upload file: http://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Upload file: https://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>


Latest revision as of 17:19, 19 February 2018

The CSDMS Help System

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

Parameter Description Unit
Input directory path to input files
Site prefix Site prefix for Input/Output files
Case prefix Case prefix for Input/Output files
Parameter Description Unit
Chezy or Manning, Chezy-1 or Manning-2 -
Parameter Description Unit
D90 of the surface mm
hydraulic radius m
Chezy coefficient -
initial depth mm
Mean diameter mm
alpha (r) -
roughness coefficient
starting point m
Slope m / m
water discharge m2 / s
step size m
Parameter Description Unit
Model name name of the model -
Author name name of the model author -

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)

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:

See also: Help:Images or Help:Movies

Developer(s)

Gary Parker

References

Key papers

Links

Any link, eg. to the model questionnaire, etc.

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