41.4 Routing - nptel - Indian Institute of Technology Madras

Hydraulics Prof. B.S. Thandaveswara
41.4 Routing
The computation of a flood wave resulting from a dam break basically involves two
problems, which may be considered jointly or seperately:
1. Determination of the outflow hydrograph from the reservoir for flow through the
breach.
2. Routing of the outflow from the dam in the downstream reach of the channel.
41.4.1 Input Required
(a) Water discharges entering into and flowing along the body of water from which the
impound water is released.
(b) Water discharges (s) flowing out from the body of water before the sudden release.
(c) Water discharges (s) flowing along the bodies of water into which impound water is
suddenly received.
(d) The flow regime (such as GVF, Uniform) associated with both the bodies which
releases and receives.
(e) Water surface elevation
(f) Submergence effect.
(g) Time function of breaching (or closing and opening of gates in canals).
The above information may be in the form of parameters or functions.
41.4.2 Breach Outflow Hydrograph
This is the outflow resulting from a dam collapse from the initiation of the breach till the
reservoir water level reaches the final breach bottom level, or the contents of reservoir
gets exhaused whichever is earlier (as in multiple breaches, the extent of breach could
be different). The breach outflow hydrograph may be obtained by using reservoir routing
method.
In case of a dam break problem, the following functions are required:
(a) Inflow hydrograph (f1 (t));
(b) Outflow hydrograph (Outflow through openings) (f2 (t));
Indian Institute of Technology Madras

Hydraulics Prof. B.S. Thandaveswara
(c) Stage hydrograph (f3(h) h is the depth);
(d) Outflow rating curve (f4 (H), H is the head); and
(e) Storage function (a function of elevation)
Reservoir routing can be accomplished with any one of the hydrologic routing methods
(puls, storage indication method) based on the equation
Indian Institute of Technology Madras
dS
= I - Q
dt
in which
I is the inflow into the reservoir, Q is the outflow from the reservoir and,
dS is the rate of change of storage in the reservoir
dt
Commonly used method is modified Puls method.
The other method for solving equation is Standard Runge - Kutta method, in which the
water surface elevation and water spread area are used. This approach does not
require the computation of special storage outflow (as in the case of modified Puls
method), but is more closely related to hydraulics of flow through the reservoir. The 3 rd
Order Runge - Kutta method involves dividing each time step interval into three
increments and calculating successive values of water surface elevation and reservoir
discharge. This method has proved to be easier for programming and computations as
the trial and error procedure is eliminated.
Determination of breach outflow hydrograph requires knowledge of rate of breaching.
Models for this purpose are available in standard commercial software.
41.4.3 Channel Routing
This is a mathematical procedure used for tracking the flow along the channel. This
involves the determination of discharge, water surface elevation, and time of arrival of
peak, along the channel reaches, by using St. Venant's equation. i.e. unsteady free
surface flow equation. One may note that, kinematic wave approximation also known as

Hydraulics Prof. B.S. Thandaveswara
lumped method routing will lead to "channel routing". Otherwise the routing using the
Saint Venant equations is called the distributed flow routing.
41.4.3.1 Boundary Condtions
Upstream Boundary: Computed breach outflow hydrograph
Downstream Boundary: The stage discharge relationship
41.4.3.2 Internal Boundary Condtions
There are many types of internal boundaries and some of them are shown in Figure
41.2.
Indian Institute of Technology Madras
Transverse Slope
Left Flood
Plain
Right Flood
Plain
Rising Flood
Falling Flood
Meandering
Main Channel
Parallel to Bank

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
Weir
Expansion or Contraction
Levee
Drops or Steps
Lock
Dam
Dam and Lock

Hydraulics Prof. B.S. Thandaveswara
Loop
Constant Level
Indian Institute of Technology Madras
Bridge
Bridge Breach
Flood
Plain
H
River
River
Formation
of Cells
1. Agricultural Land
2. Urban Land (Islands)
2__
3 H
Intake Flow
Intake
Figure 41.2 - Some of the Interior Boundaries
Emabankment
Flood Detention Basin
Existing Levee
Intake for detention basin
acts as a weir-bi-directional flow
Possible Super Critical Flow

Hydraulics Prof. B.S. Thandaveswara
41.4.3.3 Information Required for Routing the Dam Break Flow
(1) The model and scheme that is to be adopted.
(2) Lateral Flow - whether distributed or lumped inflow and outflow and its
characteristics with respect to time. The lateral flows include
(i) Contribution of rainfall on the free surface
(ii) Overland flow
(iii) Infiltration
(iv) Evaporation
(v) Seepage
(3) Cross sectional details
(a) Prismatics or (b) Non-uniform properties of natural rivers.
Following methods are used for representing the cross sections
Replacing of actual river by unform channel for total length such as Trapezoidal section.
Indian Institute of Technology Madras
• Repacing of actual river by series of prismatic channel.
• Representing cross sections by Polygonal sections.
• Replacing of surveyed sections by Polynomials.
• Interpolation of cross sections.
• Stochastic generation of cross sections.
(4) RESISTANCE PROPERTIES:
Any resistance law such as Chezy's, Manning's, Darcy- Weisbach's may be used. The
relevant coefficients need to be defined as a function of length (or section) and its
variational function with respect to depth should be known.
(5) Details of channel network in Flood plains
41.4.3.4 : Numerical Methods for Solving the Governing Equations
Any of the following numerical methods may be used for solving the governing Saint-
venant equations in conservation form. Many schemes such as Total Variation
Diminishing (TVD), Essentially Non-Oscillating (ENO) have been proposed in recent
years for correct numerical solution of the governing equations.

Hydraulics Prof. B.S. Thandaveswara
(i) Explicit - Lax Wendroff
(ii) Diffusive scheme
(iii) Method of characteristics - irregular grid using predictor - corrector scheme.
(iv) Explicit with - Two dimensional characteristic Network model with moving grid -
Reservoirs as nodes channels as links.
(v) Four point implicit (nonlinear Finite Difference Scheme)
(vii) Galerkin Finite element method
41.4.3.5. Steps in Mathematical Formulation
1. To identify the model and technique to be used.
2. INPUT THE DATA regarding
(a) Physical system (Figure 41.3) including internal boundaries.
Q
Inflow Hydrograph
Indian Institute of Technology Madras
t
Reservoir
Spillway
Tributary
Bridge
Over topping
Piping
Cells

Hydraulics Prof. B.S. Thandaveswara
Indian Institute of Technology Madras
11 31
21
Branched
Looped
Figure 41.3
(b) Types of precipitation distribution, Spillway rating curve.
Cell groups
(Two dimensional)
(c) Shape, size and progress of breach with time or piping, time of starting of breach.
3. To write the finite difference approximations for all situations that are to be
incorporated.
4. To choose the method of averaging the Sf Arithmetic, Geometric, Harmonic).
5. Softwares regarding Newton Raphson technique, Matrix method, Space matrix
converter to normal matrix, (if possible) such as Band solver and program for reservoir
routing, dynamic channel routing, are required.
41.4.4 Available Software
Two models namely HEC Dam break model and, DAMBRK / DWOPER models
developed by Fread for National weather service are available for dambreak flow
analysis. A new model FLDWAV has been developed in 1985 by Fread.
The FLDWAV model is a system of DWOPER and DAMBRK. This is a generalised
dynamic wave model for one dimensional unsteady flows in a single or branched water
way. It is based on Four point nonlinear implicit F.D. model. The following special
features are included in that model.
(i) Variable ∆t and ∆x grid.
(ii) Irregular cross sectional geometry.
(iii) off channel storage.

Hydraulics Prof. B.S. Thandaveswara
(iv) Roughness coefficient as a function of discharge on water surface elevation and
along the distance.
(v) Linearly interpolated cross sections and roughness coefficients.
(vi) Automatic computation of initial steady state.
(vii) Time dependent leteral flows.
(viii) Can account for Supercritical/ Subcritical flows.
Indian Institute of Technology Madras