Floodplain Section
• 15 Aug 2022
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# Floodplain Section

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Article Summary

The Floodplain Section calculates the flow along a floodplain. It will typically be used to connect two Reservoirs, which represent storage on the floodplain, but can also be used to model lateral flows such as those over embankments, under weirs or friction-flow conditions, and in-line flows where normal depth conditions prevail.

## Data

Field in Data Entry Form

Description

Name in Datafile

Upstream

First label

Label1

Downstream

Second label

Label2

Calibration  Coefficient

Weir coefficient (includes discharge, velocity and calibration coefficients)

Cd

Modular Limit

Modular limit (eg 0.9)

m

Floodplain Separation – Upstream

Distance from centre of upstream cell to section (m)

d1

Floodplain Separation - Downstream

Distance from section to centre of downstream cell (m)

d2

Force Friction Flow

Optional keyword 'FRICTION' to force friction flow for all segments

friction

D/S Area Constraint

Minimum value of downstream area (relative to upstream area) when Manning’s equation applies. Typical value 0.1.

ds_constraint

n/a

Number of ensuing data lines

n

Chainage

Chainage along section at which yi is defined (m)

xi

Elevation

Ground elevation at chainage xi (mAD)

yi

Manning’s n

Manning's n roughness coefficient between chainages xi and xi+1

ni

## Theory and Guidance

The Floodplain Section calculates the flow along a floodplain. Typically, the Floodplain Section will be used to connect two Reservoirs, which represent storage on a floodplain. The Floodplain Section can also be used to model lateral flows such as those over embankments, under weir or friction-flow conditions, and in-line flows where normal depth conditions prevail. The Floodplain Section incorporates the weir-type flow capability of the Spill as well as friction-type normal depth flow.

The Floodplain Section operates by splitting the cross-section into a number of segments defined by the points supplied by you, and other points where flow conditions change. The flow is calculated for each segment using Manning's equation or an integrated form of the weir equation for free or drowned flow. The Floodplain Section can be forced to operate exclusively using Manning's equation, or it can be allowed to switch between Manning's equation and weir flow. In the latter case, the lower of the discharges calculated using the two methods will be chosen for each segment. These flows are then summed together, subject to stability constraints, to give values over the entire section.

The Floodplain Section is connected to other units in exactly the same way as the SPILL unit, and can depend on water levels at two, three, or four nodes.

For instance, if the Floodplain Section unit is connected between two reservoir units, representing flood cells, the unit operates in much the same way as a weir, the two node labels being associated with the reservoir nodes.

If the Floodplain Section unit is used to represent flow between a channel and an area of static storage such as a reservoir unit, one node label is coincident with the spill label of the associated river unit, and the other with the reservoir unit. The flow is then dependent on the water levels at the associated river unit, the corresponding unit downstream of this, and the reservoir.

If the Floodplain Section unit is used to model lateral flow between two channels, each node label is coincident with the spill label of the associated river unit in each channel. The flow is then dependent on the water levels at the associated river units, and each of their corresponding downstream units.

The unit requires the user to specify a set of offset/elevation pairs which describe a traverse of the floodplain or the crest of the bank. If the unit is being used to model flow over the bank of a channel then it is usual for the total distance (offset) of the spill to be equal to the distance between the adjacent RIVER sections.

For each offset/elevation pair, a roughness parameter is required, as in the RIVER SECTION unit. The roughness value given for a point will apply to the portion of the section up to the next defined point. The roughness value given for the last point on the section is a dummy value. Panel markers, which are used in RIVER SECTION units, are not required, as each segment between data points effectively operates as a panel.

When operating in friction flow mode, a distance across the unit is required for the calculation of the water surface slope. If the unit is being used to represent flow between two RESERVOIRS, then the distance should be measured from the centre of the upstream cell to the centre of the downstream cell. If the unit is modelling flow over an embankment, then the distance should be measured from the centre of the channel to the centre of the adjacent floodplain. If the unit is positioned between two river sections, then the physical distance between the upstream and the downstream surveyed sections should be used.

Further discussion of the operation in weir-type mode can be found in the documentation for the Spill unit.

### Equations

#### Mode 0 - Zero Flow

Condition

The upstream (highest) water level is below the ground level defined in the floodplain section, or the water levels are above the ground level but almost exactly equal, or friction flow has been forced by the user and n=0.

Equation

 q = 0

where:

q = flow over segment

#### Mode 1 - Free Weir Flow (positive sense)

The general equations are the same as those given in the documentation for the Spill with Mode 1 flow. The equations given here assume that the Floodplain Section is connected between two Reservoirs .

Condition

Equation

 qs = Cd b y1 Öy1 (1)

where:

y1 = water depth above section in upstream cell

y2 = water depth above section in downstream cell

m = modular limit

b = width of segment

#### Mode 2 - Drowned Weir Flow (Positive Sense)

The general equations are the same as those given for the Spill with Mode 2 flow. The equations given here assume that the Floodplain Section is connected between two Reservoirs .

Condition

Equation

 (2)

where:

y1 = water depth above section in upstream cell

y2 = water depth above section in downstream cell

m = modular limit

b = width of segment

#### Mode 3 - Free Weir Flow (Negative Sense)

The same formulae apply as for Mode 1, but with y2 interchanged with y1.

#### Mode 4 - Drowned Weir flow (Negative Sense)

The same formulae apply as for Mode 2, but with y2 and y1 interchanged.

#### Mode 5 - Friction Flow (Positive Sense)

Condition

qf  <  qs

or

friction flow forced and n > 0

Equation

 (3)

where:

 A = (d2 (y11 + y12) + max (m d2 (y11 + y12), d1 (y21 + y22))) b/2d (4)
 P = ((gl1 - gl2)2 + b2)½ (5)
 s = ((y11 + y12) - (y21 + y22)) / (2d) (6)

For flow between two floodplain cells, these simplify to:

 A = (d2 y1 + max (m d2y1, d1 y2)) b/d (7)
 s = (y1 - y2) / d (8)

where:

y1 = water depth above section in upstream cell

y2 = water depth above section in downstream cell

gl1 = ground level at left-hand end of segment

gl2 = ground level at right-hand end of segment

d1 = distance from centre of upstream cell to section

d2 = distance from section to centre of downstream cell

d = d1 + d2

m = modular limit

n = Manning's roughness coefficient

b = width of segment

d = distance between cell centres

y11, y12, y21, y22 are defined as in the Spill unit.

#### Mode 6 - Friction Flow (Negative Sense)

The same formulae apply as for Mode 5 but with y21 and y11 interchanged, y12 and y22 interchanged and y2 and y1 interchanged.

In all cases, the smaller of qs (spill- or weir-type flow) and q(friction-type flow) is chosen.

### General

The unit mode shows the proportion of the section which is conveying friction-based flow. Thus if it is zero then the whole structure is operating as a weir, and if it is unity then the whole structure is operating using Manning's equation.

The unit state shows the average water level used for the calculation of friction flow through the section.

If part of the section has a Manning's roughness value of zero specified, then that part will always operate as a weir. If, in addition, the keyword FRICTION is used to force friction flow for the whole section, then any part of the section with zero roughness will convey no flow.

The equation for friction flow calculates the flow area using a weighted average of the upstream and downstream water levels. If the downstream level were very low, however, this might give a negative flow area. The equation for A in Mode 5 flow therefore uses the upstream water depth multiplied by the downstream area constraining factor if this is larger than the downstream water depth. To minimise the impact of this for higher downstream water level conditions, this value should generally be set fairly low, for example 0.1. The average depth used in this calculation is output as the unit state for this unit.

For any part of the section where both weir-type and friction-type flow are possible, both will be calculated and the smaller of the two discharges will be chosen.

The local relaxation which applies to the spill unit also applies to the floodplain section unit. Details can be found in the Spill unit topic.

The two labels for a floodplain section unit must be positioned together in the initial conditions in the datafile.

## Datafile Format

Line 1 - keyword 'FLOODPLAIN' [comment]

Line 2 - keyword 'SECTION'

Line 3 - Label1, Label2

Line 4 - Cd, m, d1, d2, [friction], ds_constraint

Line 5 - n

Line 6 to Line 5+n - xi, yi, ni

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