Siphon Spillway
    • 21 Sep 2022
    • 3 Minutes to read
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    Siphon Spillway

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    Article Summary

    This unit models flow through a self-priming siphon spillway. A siphon is essentially a short discharge conduit located above the hydraulic grade line. The existence of sub-atmospheric pressure allows water to be sucked up above the upstream free surface level before it is discharged at a lower level downstream.

    Data

    Field in Data Entry Form

    Description

    Name in Datafile

    Node 1

    Upstream node label

    Label1

    Node 2

    Downstream node label

    Label2

    Crest Level

    level of weir crest (mAD)

    Zc

    Soffit Level

    level of soffit of hood (mAD)

    zsoff

    Bore Area

    bore area of syphon (m2)

    Area

    Max Hood Level

    maximum hood level (for weir flow over hood) (mAD)

    zmax

    Weir Discharge Coefficient

    Discharge coefficient for weir flow over crest

    CWeir

    Pipe Discharge Coefficient

    Discharge coefficient for pipe or blackwater flow

    Cfull

    Modular Limit

    Modular limit

    m

    Prime Level

    level on the upstream side at which the syphon becomes fully primed (m AD)

    zprime

    Theory and Guidance

    The Siphon Spillway unit models flow through a self-priming siphon spillway.

    A siphon is essentially a short discharge conduit located above the hydraulic grade line. The existence of sub-atmospheric pressure allows water to be sucked up above the upstream free surface level before it is discharged at a lower level downstream.

    Several types of flow are possible through a siphon spillway. If the upstream water level is below the soffit of the inlet but above the invert, gravity spillway flow occurs for which the equation for a broad crested weir is used. Once the inlet is submerged there is a transitional flow regime as the siphon becomes primed. This is modelled as a weighted average between the limiting cases of weir flow and pipe (or blackwater) flow to ensure continuity of flow. When the upstream water level exceeds the user defined primary level, pipe flow prevails. When the upstream level exceeds the maximum hood level, the flow is supplemented by spillage over the hood which is also modelled by the broad crested weir equation.

    Equations

    Mode 1 - Dry sill

    Condition

    y1 - zc < 0

    Equation

    Q = 0

    Mode 2 - Free weir flow

    Condition

    y1 - Zc > 0

    y1 £ Zsoff

    ( (y1 - Zc) / (y-Zc) ) > m

    Equation

    Q = 0.544 Cweir b Ög (y1 - zc)1.5

    (1)

    where:

    b = breadth of siphon (normal to the flow) (m)

    RiverNodesimagesSiphon1.gifFigure 1: Free Weir Flow (Mode 2)

    Mode 3 - Drowned weir flow

    Condition

    y1 - Zc> 0

    y1 £ zsoff

    ( (y1 - Zc) / (y-Zc) ) £ m

    Equation

    Q = 0.544 Cweir b Ög (y1 - Zc)1.5 drownf

    (2)

    where:

    drownf = (1 - (y- Zc) / (y1 - Zc)) / (1 - m)

    Mode 4 - Transitional flow regime

    Condition

    y1 > zsoff

    y1 < zprime

    Equation

    Q = (y1 - Zc) (Qblack - Qweir) / (zprime - zsoff) + Qweir

    (3)

    where:

    zprime = level on the upstream side at which the siphon becomes fully primed (mAD)

    Qblack = 0.799 Cfull Area Ö(2g) (zprime - y2)0.5

    Qweir is defined in equation (2)

    Mode 5 - Pipe or blackwater flow

    Condition

    y1 > zprime

    y1 < zmax

    Equation

    Qblack = 0.799 Cfull Area Ö (2g) (y1 - y2)0.5

    (4)


    RiverNodesimagesSiphon2.gifFigure 2: Pipe or Blackwater Flow (Mode 5)

     Mode 6 - Free flow over hood and through siphon


    Condition

    y1 > zmax

    ( (y1 - zmax) / (y2 - zmax) ) > m

    Equation

    Q = Qblack + 0.544 Cweir b Ög (y1 - zmax)1.5

    (5)

    where:

    Qblack is defined in equation (4)

    Mode 7 - Drowned flow over hood and through siphon

    Condition

    y1 > zmax

    ( (y1 - zmax) / (y2 - zmax) ) £ m

    Equation

    Q = Qblack + 0.544 Cweir b Ög (y1 - zmax)1.5 drownf

    (6)

    where:

    drownf = (1 - (y2 - zmax) / (y1 - zmax)) / (1 - m)

    Qblack is defined in equation (4)

    General

    Reverse flows are precluded for syphonic weirs in all run modes - they should never occur for any siphon operating as intended. Flood Modeller will stop running a simulation and produce an error message if this is predicted to occur.

    Priming usually occurs when the upstream water level has risen to not more than about one third of the throat height, but the precise level will depend on the particular siphon design.

    As the upstream water level reaches the priming level a sudden increase in flow is observed in practice. This increase in flow is modelled as a more gradual process in this unit by the assumption of a weighted linear average of weir and blackwater flow.

    Datafile Format

    Line 1 - keyword 'SYPHON'

    Line 2 - Label1, Label2

    Line 3 - zc, zsoff, Area, zmax

    Line 4 - CWeir, Cfull, m, zprime

    Example

    SYPHON
    UNIT031     UNIT032
         1.000     2.000     2.000     3.000
         0.900     0.900     0.900     0.500

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