Rectangular Conduit
    • 21 Oct 2022
    • 4 Minutes to read
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    Rectangular Conduit

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    Article summary

    The Rectangular Conduit models rectangular cross section closed conduits or culverts. The cross section is specified by the invert level, width and height of the conduit.

    Data  

    Field in Data Entry Form

    Description

    Name in Datafile

    Section Label

    Node label

    Label1

    Distance to Next Conduit

    Distance to next section downstream (m)

    dx

    Equation

    Either "MANNING" or "COLEBROOK-WHITE" to specify the form of friction equation to be used

    frform

    Elevation of Invert

    Invert level (metres above datum)

    inv

    Width

    Width of conduit (m)

    width

    Height

    Height of conduit (ie the distance between the culvert invert and the soffit (m)

    height

    Value on Invert

    Friction coefficient on invert of conduit (in units of metres if Colebrook-White is used)

    fribot

    Value on Sidewalls

    Friction coefficient on sidewalls of conduit (in units of metres if Colebrook-White is used)

    frisid

    Value on Soffit

    Friction coefficient on soffit of conduit (in units of metres if Colebrook-White is used)

    fritop

    Use Bottom Slot

    Choose whether to include a bottom slot or to use the model default (global) (bslot=('ON', 'OFF' or 'GLOBAL'(default)).

    bslot

    Distance of slot top

    Height of the top of the bottom slot with respect to the culvert invert (m). If zero, the default value will be used; if negative, the global value will be used.

    dh

    Total depth of Bottom Slot

    Total depth of the bottom slot (m). If zero, the default value will be used; if negative, the global value will be used

    dslot

    Use Top Slot

    Choose whether to include a top slot or to use the model default (global) (tslot='ON', 'OFF' or 'GLOBAL'(default)).

     tslot

    Distance of slot bottom

    Depth of the bottom of the top slot relative to the culvert soffit (m). If zero, the default value will be used; if negative, the global value will be used.

    dh_top

    Total height of Top Slot

    Total height of the top slot (m). If zero, the default value will be used; if negative, the global value will be used

    hslot

    Theory and Guidance

    The Rectangular Conduit models rectangular cross section closed conduits or culverts in either free surface or pressurised flow modes.

    The cross section is specified by the invert level, width and height of the conduit. Three friction factors are specified - one each for the bottom, sides and top of the conduit.

    A minimum of two Rectangular Conduits are required, one for each end of the conduit reach. Intermediate cross sections can be specified by additional Rectangular Conduits or by using Replicated units.

    The width and height may change between sections, although the Pseudo-Timestepping Method will have to be used for steady state simulations, as the Direct Method cannot solve for this situation. This is also true for friction values that vary along the conduit reach.

    Both free surface and pressurised flows are allowed. The pressurised flow approach is particularly appropriate for hydraulically long culverts, but may not be suitable in situations which approximate to orifice flow in a short culvert. A general alternative for short culverts is the Bernoulli Loss, but an Orifice would be preferable in many cases since it specifically models orifice flow.

    The Rectangular Conduit is based on the Saint-Venant equations which express the conservation of mass and momentum of the water body. Pressurised flow is accommodated through incorporation of an infinitesimally thin frictionless slot in the top of the conduit, known as a Preissmann Slot , so that the water level calculated by the program is the piezometric level. This means that the cross-sectional area and the conveyance remains unaltered if the water level rises above the soffit level.

    Localised regions of supercritical flow can be modelled approximately.

    Equations

    The equations used in the Rectangular Conduit are the mass conservation or continuity equation:

     

    mass_conservation(3)

    (1)

    where:

    Q = flow (m3/s)

    A = cross section area (m2)

    q = lateral inflow (m3/s/m)

    x = longitudinal channel distance (m)

    t = time (s)

    and the momentum conservation or dynamic equation:

     

    momentum_conservation(3)

    (2)

    where:

    h = water surface elevation above datum (m)

    ß = momentum correction coefficient

    g = gravitational acceleration (m/s2)

    k = channel conveyance. Channel conveyance can be calculated using Manning's equation or the Colebrook White equation. See Conduit Channel Conveyance.

    General

    Steep sloping conduits will need closer cross section spacing than mild sloping culverts.

    Exit and entry losses (and any abrupt intermediate contractions or expansions) are not covered by the Rectangular Conduit and may be included explicitly using the Culvert Inlet and Culvert Outlet or Bernoulli Loss, for example.

    Critical depth control at entry or exit and entrance geometry control are not included. These flow modes can be approximated by inclusion of some sort of Weir at entry or exit or by use of an Orifice at the entrance (or an orifice alone for a hydraulically short culvert).

    Connectivity Rules

    Rectangular Conduits should not be connected directly to:

    You can connect different types of reach using a Junction if no head loss occurs at the join. Alternatively the specialised Culvert Inlet and Culvert Outlet can be used to model the losses associated with transitions from open channel to culverts and vice versa. Bernoulli Losses are also available to model more generalised losses.

    Datafile Format

    Line 1 - keyword `CONDUIT' [comment]

    Line 2 - keyword `RECTANGULAR'

    Line 3 - Label1

    Line 4 - dx

    Line 5 - frform

    Line 6 - inv, width, height, bslot, dh, dslot, tslot, dh_top, hslot

    Line 7 - fribot, frisid, fritop

    Lines 1 to 7 are repeated n times, one for each distance step. A dx value of zero signifies the end of the conduit "reach".

    RiverNodesimagesCondRectangularData.gif



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