 21 Sep 2022
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Siphon Spillway
 Updated on 21 Sep 2022
 3 Minutes to read

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This unit models flow through a selfpriming siphon spillway. A siphon is essentially a short discharge conduit located above the hydraulic grade line. The existence of subatmospheric 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)  Z_{c} 
Soffit Level  level of soffit of hood (mAD)  z_{soff} 
Bore Area  bore area of syphon (m^{2})  Area 
Max Hood Level  maximum hood level (for weir flow over hood) (mAD)  z_{max} 
Weir Discharge Coefficient  Discharge coefficient for weir flow over crest  C_{Weir} 
Pipe Discharge Coefficient  Discharge coefficient for pipe or blackwater flow  C_{full} 
Modular Limit  Modular limit  m 
Prime Level  level on the upstream side at which the syphon becomes fully primed (m AD)  z_{prime} 
Theory and Guidance
The Siphon Spillway unit models flow through a selfpriming siphon spillway.
A siphon is essentially a short discharge conduit located above the hydraulic grade line. The existence of subatmospheric 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  y_{1}  z_{c} < 0 
Equation  Q = 0 
Mode 2  Free weir flow
Condition  y_{1}  Z_{c} > 0 y_{1} £ Z_{soff} ( (y_{1}_{ } Z_{c}) / (y_{2 }Z_{c}) ) > m  
Equation 
where: b = breadth of siphon (normal to the flow) (m) 
Mode 3  Drowned weir flow
Condition  y_{1}  Z_{c}> 0 y_{1} £ z_{soff} ( (y_{1}  Z_{c}) / (y_{2 }Z_{c}) ) £ m  
Equation 
where: drownf = (1  (y_{2 } Z_{c}) / (y_{1}  Z_{c})) / (1  m) 
Mode 4  Transitional flow regime
Condition  y_{1} > z_{s}_{off} y_{1} < z_{prime}  
Equation 
where: zprime = level on the upstream side at which the siphon becomes fully primed (mAD) Q_{black}_{ }= 0.799 C_{f}_{ull} Area Ö(2g) (z_{prime}  y_{2})^{0.5} Q_{weir} is defined in equation (2) 
Mode 5  Pipe or blackwater flow
Condition  y_{1} > z_{prime} y_{1} < z_{max}  
Equation 

Mode 6  Free flow over hood and through siphon
Condition  y_{1}_{ }> z_{max} ( (y_{1}_{ } z_{max}) / (y_{2}_{ } z_{max}) ) > m  
Equation 
where: Qblack is defined in equation (4) 
Mode 7  Drowned flow over hood and through siphon
Condition  y_{1}_{ }> z_{max} ( (y_{1}_{ } z_{max}) / (y_{2}_{ } z_{max}) ) £ m  
Equation 
where: drownf = (1  (y_{2}_{ } z_{max}) / (y_{1}_{ } z_{max})) / (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  z_{c}, z_{soff}, Area, z_{max}
Line 4  C_{Weir}, C_{full}, m, z_{prime}
Example
SYPHON
UNIT031 UNIT032
1.000 2.000 2.000 3.000
0.900 0.900 0.900 0.500