Model help:BackwaterCalculator

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

Input Files and Directories

Run Options

Run Parameters

About

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)

Nomenclature

Symbol	Description	Unit
x	Streamwise coordinate	L
ΔX	Spatial step length	L
S	bed slope	-
Sf	friction slope	-
Fr	Froude number	-
Cf	non-dimensional friction coefficient	-
g	acceleration of gravity	L / T2
Cz	non-dimensional Chezy friction coefficient	-
Kcz	dimensional Chezy friction coefficient	-
αr	user specified parameter	-
ks	roughness height due to skin friction	L
nk	non-dimensional order-one constant	-
H1	starting water depth at the downstream end of the channel	L
x1	starting position	L
qw	water discharge per unit width	L2 / T
D90	diameter of the bed surface such that 90% of the distribution is finer	L
Cf	Non-dimensional friction coefficient	-

Output

Symbol	Description	Unit
H	water depth	L
U	mean flow velocity	L / T
η	bed elevation	L
Hn	water surface at normal flow	L
Hc	critical water depth	L
τb	shear stress	-
Frn	Froude number at normal flow	-
Un	mean flow velocity at normal flow	L / T
Uc	critical flow velocity	L / T
τbn	bed shear stress at normal flow	-
ξ	water surface elevation	L

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_r and n_k 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: https://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)

Gary Parker

References

Key papers

Links

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