Normal/Critical Depth Boundary
    • 21 Sep 2022
    • 6 Minutes to read
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    Normal/Critical Depth Boundary

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    Article summary

    The Normal/Critical Depth Boundary (NCDBDY) unit is a downstream boundary which automatically generates a flow-head relationship based on section data. The options available are to apply normal depth (from Manning's equation), or critical depth. This is a simpler alternative to the QHBDY in which the rating table is explicitly supplied.

    Data

    Field in Data Entry Form

    Description

    Name in Datafile

    Boundary Unit Label

    Boundary node label

    Label 1

    Downstream Node

    Not used - leave blank

    Label 2

    Remote Label 1

    Remote node label #1 (optional) - used to provide section data and downstream slope extent (the latter used for NORMAL depth only)

    Label 3

    Remote Label 2

    Remote node label #2 (NORMAL depth only; optional) upstream slope extent

    Label 4

    Boundary Type Flag

    Boundary type - 'NORMAL' or 'CRITICAL' [depths]

    ctype

    Slope Calculation

    Slope calculation method - used for Normal depth calculations only, determines whether the slope used is calculated from the Bed slope, Water Surface slope or User defined.

    slptyp

    Slope Value/ Gradient

    If user-defined, enter the value of the slope here. The slope value is teh absolute value of the slope; the Gradient, x, is specified as 1 in x, i.e. Slope Value = 1/Gradient. A 1:100 slope therefore has a Slope Value of 0.01 and a Gradient value of 100. NB Only one of these values needs entering.

    slope

    Number of Data Points

    Number of ensuing section data points (set to zero if section data obtained from existing channel section)

    ndat

    Section Data (x,y,n)

    Cross chainage (m), elevation (m AOD) and Manning's n of cross-section to be used (if not obtained from existing channel section)

    xi, yi, ni

    Panel Marker

    Panel marker - '*' to denote panel separator, blank otherwise

    panel

    Theory and Guidance

    The Normal/Critical Depth Boundary (NCDBDY) unit enables the user to specify a downstream boundary, which automatically generates a flow-head relationship based on section data. The options available to the user are to apply normal depth (from Manning's equation), or critical depth. This facility is a simpler alternative to the QH boundary, in which the rating table is explicitly supplied by the user.

    The NCDBDY may be specified as usual within the data file, or may also be specified in an external Flood Modeller Event Data (*.ied) file to override the downstream boundary in the data file.

    Section data may be obtained from existing river or conduit units, or may be explicitly provided by the user within the unit.

    Connectivity (Node labelling)

    1. In its simplest form, only the first node label is required - that of the boundary.
    2. The second node label is reserved for future use as a two-noded unit and should be left blank.
    3. The third node label (remote node label) is used to specify a node other than the boundary node from which to extract section data. This is essential if the boundary node is not directly connected to a channel section unit and the section data is not specified explicitly within the unit. If specified, this node will also be used as the downstream extent when determining the slope (Normal depth, automatic slope calculation only).
    4. The fourth node label is only used for Normal Depth in automatic slope calculation mode (Bed or Water Surface). This denotes the upstream extent of the slope used (see Figure 1). There must be a simple path to the downstream extent via channel sections and two-noded structures. A junction or reservoir is only permitted in this path if it is directly connected to the downstream extent node.

    RiverNodesimagesNormalCriticalBdy2.gif

    Figure 1: NCDBDY upstream slope extent label usage example. The slope used is denoted by the red line. If the upstream extent node is not specified, the boundary will use the slope from node2 to node1.

    Data input

    Main Data tab

    RiverNodesimagesNormalCriticalBdy3.gif

    The main data tab requires the user to select whether Normal or Critical Depth should be applied at the boundary, and if Normal Depth is selected, the method of slope calculation as follows:

    • Bed - the slope is calculated from the difference in lowest bed elevations (or bed marker elevations, if specified) at the given two extents.
    • Water Surface - the slope is calculated from the difference in water levels ) at the given two extents.
    • User - the user enters a fixed value for the slope, either as an absolute value or as n in a 1-in-n format. For instance, for a 1:1000 slope, enter 0.001 as the Slope Value or 1000 for the Gradient value. Only one value need be entered - the other is automatically updated. The slope must be positive.

    For the automatically generated slopes (i.e. Bed and Water Surface), the slope extents are taken from Node Label 1 or 3 (downstream) and Node Label 4 (upstream). If node label 4 does not exist, then the upstream extent is assumed to be the channel node immediately upstream of the downstream extent. For an irregular longitudinal bed profile, it is recommended that the user select an upstream slope extent (see Node labelling, item 4) several nodes upstream to nullify localised effects.

    NB Since it is dependent on the water level at two locations, selecting a Water Surface slope can result in a non-unique Normal Depth. The value obtained depends largely on the initial conditions.

    Section Data tab

    RiverNodesimagesNormalCriticalBdy4.gif

    The Section Data tab is only required if the section data used is to be explicitly specified within the NCDBDY unit, as opposed to being obtained from an existing river or conduit section.

    To activate this option, the "Specify Section Data" box should be checked and the section data entered as per a simplified Flood Modeller River unit. Mandatory fields are cross chainage (x-value) and elevation (y-value). Additionally, for Normal Depth, Manning's n is required, and the provision of panel markers (see RIVER unit) is available.

    Equations and formulation

    Normal depth

    The condition to be satisfied for normal depth to apply is Manning's equation:

    NormalCriticalBdyEqn1

    (1)

    where

    Q is the flow (m3s-1)

    K is the conveyance (m3s-1)

    S is the channel slope

    If the slope is generated automatically, then:

    NormalCriticalBdyEqn2

    (2)

    where

    y0 and y1 are the lowest section elevations or water levels of the downstream and upstream slope extents, respectively

    NormalCriticalBdyEqn3is the longitudinal distance between them

    The conveyance is calculated exactly as in the RIVER or CONDUIT unit.

    Critical depth

    The condition to be satisfied for critical depth to apply is that the Froude number is equal to unity, i.e.

    NormalCriticalBdyEqn4

    (3)

    where

    b is the channel wetted width (m)

    Q is the flow (m3s-1)

    g is the acceleration due to gravity (taken as 9.81ms-2)

    A is the wetted area (m2)

    Notes

    1. Flood Modeller boundary conventions will be observed, i.e. if the NCDBDY is directly attached to a junction or reservoir, results showing positive flow denote flow into the system, and those showing negative flow denote flow out of the system.
    2. Uniqueness and existence of solutions: multiple solutions to Manning's equation are possible, in particular with gradually closed-top conduits, or when selecting Water Surface slope. There is no hard and fast rule to guarantee which solution will be returned. Solutions may not always be possible, e.g. normal depth for a conduit where flow exceeds the maximum value of , critical depth for a rectangular conduit in which free surface flow is always supercritical. In such cases, an error or approximate depth will result.
    3. Unstable models may result in negative flow or unreasonably high flow at the downstream boundary - this may cause the model to fail with a "number out of range" error at or near the NCDBDY unit.

    Datafile Format

    Line 1 : keyword 'NCDBDY', ' #revision#1', [comment]

    Line 2 : Label 1, [Label 2, Label 3, Label 4]

    Line 3 : ctype

    Line 3a : slptyp, [slope] (this line only read if ctype='NORMAL')

    Line 4 - ndat

    Line 5 to Line 4+ndat : xi, yi, ni, panel

    Line 5+ndat : novdat, [tm], [repeat], ovrmth

    Line 6+ndat to Line 6+ndat+novdat : hj, tj

    Example

    NCDBDY #revision#1
    UNIT089
    NORMAL
    AUTO             BED
             4
         0.000     2.000     0.020*
         1.000     0.000     0.020
         2.000     0.000     0.020
         3.000     2.000     0.020*
             1     HOURS    EXTENDNOOVERRIDE     0.000LINEAR
         0.000     0.000

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