# 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

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
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
 $\displaystyle{ {\frac{dH}{dx}} = {\frac{S - S_{f}}{1 - Fr^2}} }$ (1)
• Friction slope
 $\displaystyle{ S_{f} = C_{f} Fr^2 }$ (2)
• Froude number
 $\displaystyle{ Fr = {\frac{q_{w}}{\sqrt{g H^3}}} }$ (3)
• Non-dimensional friction coefficient
 $\displaystyle{ C_{f} = {\frac{1}{Cz^2}} }$ (4)
• Chezy equation
 $\displaystyle{ Cz = {\frac{K_{Cz}}{\sqrt{g}}} }$ (5)
• Manning-Strickler formulation
 $\displaystyle{ C_{f} ^ \left ( {\frac{-1}{2}} \right ) = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) }$ (6)
• Roughness height due to skin friciton
 $\displaystyle{ k_{s} = n_{k} D_{90} }$ (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: