Orifice

Data

Theory and Guidance

Datafile Format

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.

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 (m AD)

zinv

 Throat Soffit Level

soffit level of culvert (m AD)

zsoff

 Bore Area

bore area of culvert (m2)

Area

 Upstream Sill Level

level of sill on upstream side of structure (m AD)

zcup

 Downstream Sill Level

level of sill on downstream side of structure (m AD)

zcdn

Opening type

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

 

Discharge coefficient: Weir Flow

Discharge coefficient for weir flow over sill (typical value=1)

Cweir

Discharge coefficient: Surcharged Flow

Discharge coefficient for surcharged flow (typical value=1)

Cfull

 Modular Limit

Modular limit (eg 0.8)

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.

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

Q = 0

Mode 1 - Flap shut or syphon unprimed

Condition

For flapped gates:

y2 - zcdn > y1 - zcdn

For inverted syphons:

2/3(y1-zinv) < h and (y2-zinv) < h

Equation

Q = 0

Mode 2 - Free weir flow through culvert

Condition

2/3(y1 - zinv) < h

(y2 - zinv) < h

(y2 - zcup) / (y1 -zcup)) < m

Equation

Q =(2/3)1.5 Ög Cweir b (y1 - zcup)1.5

where:

b = breadth of culvert (normal to the flow) (m) (=Area/h)

Mode 3 - Drowned weir flow through culvert

Condition

2/3(y1 - zinv) < h

y2 - zinv < h

(y2 - zcup) / (y1 - zcup) > m

Equation

Q = (2/3)1.5 Ög Cweir b (y1 - zcup)1.5 drownf

where:

drownf = Ö[(1 - (y2 - zcup)/(y1 - zcup)) / (1 - m)]

or

drownf = (1 - (y2 - zcup)/(y1 - zcup))/ (0.3* (1 - m))

if the first formula for drownf gives drownf<0.3

Mode 4 - Orifice flow

Condition

2/3(y1 - zinv) > h or y2 - zinv > h

Equation

Qori = 0.799 Ö(2g) Cfull Area (y1 - zinv - hx)0.5

where:

Area = bore area of culvert (m2)

hx = max (0.8h, y2 - zinv)

or for inverted syphons:

Q = min (Qsyph, Qori)

where:

Qsyph is defined as in Mode 2 - Free Weir Flow Equation

Qori is defined as in Mode 4 - Orifice flow

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 drownf 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 drownf=0.3 and drownf=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, 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

Line 5 - Cweir, Cfull, m