# 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)