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

First tab header

Second tab header

Etc. tab header

Parameter	Description	Unit
First parameter	Description parameter	[Units]

Parameter	Description	Unit
First parameter	Description parameter	[Units]

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

[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

[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	-
D90
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	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

• Note on equations

To compute the water depth, H, everywhere in the channel for a given water discharge per unit channel width, q_w, 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_f, 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_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: 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)

Gary Parker

References

Key papers

Links

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