Orifice
    • 16 Aug 2022
    • 6 Minutes to read
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    Orifice

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    Article summary

    The Orifice models flow through an orifice, short culvert, flood relief arch, outfall or inverted syphon using either the equations for weir control or surcharged flow depending on the upstream and downstream water levels. Click the links below to navigate to the various sections of this help:

    Data

    Field in Data Entry Form

    Description

    Name in Datafile

    Upstream

    Upstream node label

    Label1

    Downstream

    Downstream node label

    Label2

    Throat Invert Level

    Invert level of culvert/orifice (mAD if metric, ft AD otherwise)

    zinv 

    Throat Soffit Level

    Soffit level of culvert/orifice (mAD if metric, ft AD otherwise)

    zsoff

    Bore Area

    Bore area of culvert/orifice (m2 if metric, ft2 otherwise) NB This is calculated by the software for a circular orifice from the soffit and invert levels (and hence orifice diameter)

    Area

    Upstream Sill Level

    Level of sill on upstream side of structure (mAD if metric, ft AD otherwise)

    zcup

    Downstream Sill Level

    Level of sill on downstream side of structure (mAD if metric, ft AD otherwise)

    zcdn

    Aperture Shape

    Shape of orifice aperture - 'RECTANGLE' [default] or 'CIRCULAR'

    shape

    Opening Type

    'FLAPPED' - does not allow reverse flows; or 'OPEN' - allows bidirectional flow

     

    Calibration Factor: Weir Flow

    Weir-type flow calibration factor. Default value 1.0, i.e. assumes a round-nosed broad-crested weir equation.

    Cweir

    Calibration Factor: Surcharged Flow

    Surcharged (orifice-type flow) calibration factor. Default value 1.0.

    Cfull

    Modular Limit

    Modular limit. Ratio of downstream to upstream head at which drowning occurs. Typical range 0.7-0.95. 

    m

    Theory and Guidance

    The Orifice models flow through an orifice, short culvert, flood relief arch, outfall or inverted syphon using either the equations for weir control or surcharged flow depending on the upstream and downstream water levels.

    Flood relief arches in the approach roads of bridges, short culverts under causeways, outfalls through longitudinal river embankments and inverted syphons are modelled using variants of the orifice equations and/or the broad crested weir equation.

    Five possible modes of flow are considered, including the cases where there is no flow. In the case where both upstream and downstream water levels are below the sill level, indeterminacy may occur - if there is another structure upstream with a closed gate, the direct method will show the stage calculated as -9999 to indicate indeterminacy.

    The culvert or orifice cross section is assumed to be rectangular by default, but circular cross-sections can also be specified.

    Reverse flow can also be modelled in unsteady mode and pseudo timestepping steady mode but not currently for the direct steady method.

    Equations

    Mode 0 - Dry sill

    Condition

    y1 - zcup < 0

    Equation

    Qdry = 0

    where:

    Qdry is the discharge,

    y1 is the upstream water elevation above the invert, and

    zcup is the level of the sill on the upstream side of the structure.

    RiverNodesimagesOrificeMode0transparent.gif

    Mode 1 - Flap shut or syphon unprimed

    Condition

    For flapped gates:

    y2 - zcdn > y1 - zcdn

    For inverted syphons:

    y- zinv ≤ 1.5h   and   y- zinv ≤ h   (rectangular)

    y- zinv ≤ 1.25d   and   y- zinv ≤ d   (circular)

    Equation

    Qflap = 0

    where:

    Qflap is the discharge,

    yis the upstream water elevation above the invert,

    yis the downstream water elevation above the invert,

    zcdn is the level of the sill on the downstream side of the structure,

    zinv is the invert level of the culvert/orifice,

    h is the total height of the orifice aperture (rectangular case), and

    d is the total diameter of the orifice aperture (circular case).

    RiverNodesimagesOrificeMode1transparent.gif

    Mode 2 - Free weir flow through culvert/orifice

    Condition

    y1 - zinv ≤ 1.5h   and   y- zinv ≤ h   (rectangular)
    y1- zinv ≤ 1.25d   and   y- zinv ≤ d   (circular)

    (y- zcup) / (y1-zcup) < m

    Equation

    Qfree = (2/3)1.5 g Cweir b (y1 - zcup)1.5 (rectangular)

    Qfree = Cweir c1 d2.5 (circular)

    where:

    Qfree is the discharge,

    yis the upstream water elevation above the invert,

    yis the downstream water elevation above the invert,

    zcup is the level of the sill on the upstream side of the structure,

    zinv is the invert level of the culvert/orifice,

    h is the total height of the orifice aperture (rectangular case),

    d is the total diameter of the orifice aperture (circular case),

    m is the modular limit,

    g is acceleration due to gravity,

    b is the breadth of the culvert/orifice (normal to the flow. m if metric, ft otherwise) (=Area/h),

    Cweir is the weir flow calibration factor, default = 1, i.e. assumes a round-nosed, broad-crested weir equation, and

    ce 1 is the product of the discharge coefficient and ᵠ factor for circular weirs (see below - NB the dimensions in the table shown have units m1/2s-1 [See Bos (1989) for further details] )

    y1/d

    0.000

    0.067

    0.134

    0.202

    0.270

    0.339

    0.408

    0.478

    0.550

    0.622

    0.696

    0.772

    0.851

    0.933

    1.020

    1.115

    1.221

    1.348

    1.520

    1.834

    ceφ1

    0.000

    0.008

    0.033

    0.074

    0.131

    0.203

    0.289

    0.389

    0.503

    0.630

    0.771

    0.925

    1.092

    1.274

    1.472

    1.690

    1.936

    2.224

    2.598

    3.210

    RiverNodesimagesOrificeMode2transparent.gif

    Mode 3 - Drowned weir flow through culvert/orifice

    Condition

    y1- zinv ≤ 1.5h   and   y- zinv ≤ h   (rectangular)

    y1- zinv ≤ 1.25d   and   y- zinv ≤ d   (circular)

    (y- zcup) / (y1- zcup) ≥ m

    Equation

    Qdrowned = Fd Qfree

    where Qfree is defined as in Mode 2 - Free Weir Flow Equation, and the drowning factor Fd is given by:

    Fd = [(1 - (y- zcup)/(y1- zcup)) / (1 - m)]

    or

    Fd = (1 - (y- zcup)/(y1- zcup))/ (0.3* (1 - m)),

    if the first formula for the drowning factor gives Fd < 0.3

    where:

    Qdrowned is the discharge,

    y1 is the upstream water elevation above the invert,

    yis the downstream water elevation above the invert,

    zcup is the level of the sill on the upstream side of the structure,

    zinv is the invert level of the culvert/orifice,

    h is the total height of the orifice aperture (rectangular case),

    d is the total diameter of the orifice aperture (circular case), and

    m is the modular limit.

    RiverNodesimagesOrificeMode3transparent.gif

    Mode 4 - Orifice flow

    Condition

    y1 - zinv > 1.5h   or   y2 - zinv > h   (rectangular)

    y1 - zinv > 1.25d   or   y2 - zinv > d   (circular)

    Equation

    Qori = Cd Cfull A √ (2g Δh)

    or for inverted syphons:

    Q = min (Qfree, Qori)

    where Qfree is defined as in Mode 2 - Free Weir Flow Equation, and  Qori is defined as in Mode 4 - Orifice flow

    where:

    Qori is the discharge,

    y1 is the upstream water elevation above the invert,

    y2 is the downstream water elevation above the invert,

    zinv is the invert level of the culvert/orifice,

    h is the total height of the orifice aperture (rectangular case),

    d is the total diameter of the orifice aperture (circular case),

    g is acceleration due to gravity,

    A is the bore area of the culvert/orifice,

    Δh is given by:

       Δh = min(y1 - y2 , y1 - 0.8h)   (rectangular hole),

       Δh = min(y1 - y2 , y1 - 0.5d)   (circular hole),

    Cd is the fixed discharge coefficient for surcharged flow given by Cd = 0.799 for a rectangular hole or Cd = 0.6 for a circular hole, and

    Cfull is the specified surcharged (orifice-type) flow calibration factor, default = 1.0.

    Note: the coefficient used within the equation is the product of the (fixed) value Cd and the (user-entered) value Cfull. If you require a different coefficient, adjust the calibration factor (Cfull) accordingly, for example a rectangle with rounded corners can be modelled using a calibration factor between 0.75 and 1.0. 

    RiverNodesimagesOrificeMode4transparent.gif

    General

    The transition from free to drowned weir flow is smooth because the modular limit remains fixed throughout the computation and is thus independent of the calculated upstream water depth.

    Reverse flow is allowed when the Flapped field is set to Open but not when set to Flapped . Reverse flow is not allowed in the direct steady method of calculation.

    For mode 4, the direct steady method always assumes the flow is governed by the orifice equation.

    The second form of the drowning factor Fd equation in mode 3 (drowned weir) flow is an approximation used to avoid an infinite derivative as the downstream and upstream levels equalise. It is a linearisation of the drowning function between Fd = 0.3 and Fd = 0.0.

    Only the upstream sill level is used in determining whether flow is possible. Thus if the upstream sill is lower than the invert level of the culvert/orifice, flow is possible even when the upstream water level is below the invert. It is recommended that the sill levels should normally be at or above the invert level to avoid unexpected results.

    Datafile Format

    Line 1 - keyword:'ORIFICE', 'INVERTED SYPHON', 'OUTFALL' or 'FLOOD RELIEF ARCH'

    Line 2 - keyword: 'FLAPPED' or 'OPEN'

    Line 3 - Label1, Label2

    Line 4 - zinv, zsoff, Area, zcup, zcdn, shape

    Line 5 - Cweir, Cfull, m

    Examples of the datafile format are given below.
    RiverNodesimagesorificeimage001.png


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