Siphon Spillway | Technical Reference

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)	Z_c
Soffit Level	level of soffit of hood (mAD)	z_soff
Bore Area	bore area of syphon (m²)	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 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 - z_c < 0
Equation	Q = 0

Mode 2 - Free weir flow

Condition

y₁ - Z_c > 0

y₁ £ Z_soff

( (y₁- Z_c) / (y₂-Z_c) ) > m

Equation

Q = 0.544 C_weir b Ög (y₁ - z_c)^1.5

(1)

where:

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

Figure 1: Free Weir Flow (Mode 2)

Mode 3 - Drowned weir flow

Condition

y₁ - Z_c> 0

y₁ £ z_soff

( (y₁ - Z_c) / (y₂-Z_c) ) £ m

Equation

Q = 0.544 C_weir b Ög (y₁ - Z_c)1.5 drownf

(2)

where:

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

Mode 4 - Transitional flow regime

Condition

y₁ > z_s_off

y₁ < z_prime

Equation

Q = (y₁ - Z_c) (Q_black - Q_weir) / (z_prime - z_s_off) + Q_weir

(3)

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 - y₂)^0.5

Q_weir is defined in equation (2)

Mode 5 - Pipe or blackwater flow

Condition

y₁ > z_prime

y₁ < z_max

Equation

Q_black = 0.799 C_full Area Ö (2g) (y1 - y2)0.5

(4)

Figure 2: Pipe or Blackwater Flow (Mode 5)

Mode 6 - Free flow over hood and through siphon

Condition

y₁> z_max

( (y₁- z_max) / (y₂_- z_max) ) > m

Equation

Q = Q_black+ 0.544 C_weir b Ög (y₁- z_max)1.5

(5)

where:

Qblack is defined in equation (4)

Mode 7 - Drowned flow over hood and through siphon

Condition

y₁> z_max

( (y₁- z_max) / (y₂- z_max) ) £ m

Equation

Q = Q_black + 0.544 C_weir b Ög (y1 - z_max)^1.5drownf

(6)

where:

drownf = (1 - (y₂- z_max) / (y₁- 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