 16 Aug 2022
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Orifice
 Updated on 16 Aug 2022
 6 Minutes to read
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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)  z_{inv } 
Throat Soffit Level  Soffit level of culvert/orifice (mAD if metric, ft AD otherwise)  z_{soff} 
Bore Area  Bore area of culvert/orifice (m^{2} if metric, ft^{2} 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)  z_{cup} 
Downstream Sill Level  Level of sill on downstream side of structure (mAD if metric, ft AD otherwise)  z_{cdn} 
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  Weirtype flow calibration factor. Default value 1.0, i.e. assumes a roundnosed broadcrested weir equation.  C_{weir} 
Calibration Factor: Surcharged Flow  Surcharged (orificetype flow) calibration factor. Default value 1.0.  C_{full} 
Modular Limit  Modular limit. Ratio of downstream to upstream head at which drowning occurs. Typical range 0.70.95.  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 crosssections 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  y_{1}  z_{cup} < 0 
Equation  Q_{dry} = 0 where: Q_{dry} is the discharge, y_{1} is the upstream water elevation above the invert, and z_{cup} is the level of the sill on the upstream side of the structure. 
Mode 1  Flap shut or syphon unprimed
Condition  For flapped gates: y_{2}  z_{cdn} > y_{1}  z_{cdn} For inverted syphons: y_{1 } z_{inv} ≤ 1.5h and y_{2 } z_{inv} ≤ h (rectangular) y_{1 } z_{inv} ≤ 1.25d and y_{2 } z_{inv} ≤ d (circular) 
Equation  Q_{flap} = 0 where: Q_{flap} is the discharge, y_{1 }is the upstream water elevation above the invert, y_{2 }is the downstream water elevation above the invert, z_{cdn} is the level of the sill on the downstream side of the structure, z_{inv} 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). 
Mode 2  Free weir flow through culvert/orifice
Condition  y_{1}  z_{inv} ≤ 1.5h and y_{2 } z_{inv} ≤ h (rectangular) y_{1} z_{inv} ≤ 1.25d and y_{2 } z_{inv} ≤ d (circular) (y_{2 } z_{cup}) / (y_{1}z_{cup}) < m 
Equation  Q_{free} = (2/3)^{1.5} √g C_{weir} b (y1  z_{cup})^{1.5}^{ }(rectangular) Q_{free} = C_{weir} c_{e }ᵠ_{1}_{ }d^{2.5}^{ }(circular) where: Q_{free} is the discharge, y_{1 }is the upstream water elevation above the invert, y_{2 }is the downstream water elevation above the invert, z_{cup} is the level of the sill on the upstream side of the structure, z_{inv} 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), C_{weir} is the weir flow calibration factor, default = 1, i.e. assumes a roundnosed, broadcrested weir equation, and c_{e}_{ }ᵠ_{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 m^{1/2}s^{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 
Mode 3  Drowned weir flow through culvert/orifice
Condition  y_{1} z_{inv} ≤ 1.5h and y_{2 } z_{inv} ≤ h (rectangular) y_{1} z_{inv} ≤ 1.25d and y_{2 } z_{inv} ≤ d (circular) (y_{2 } z_{cup}) / (y_{1} z_{cup}) ≥ m 
Equation  Q_{drowned}_{ }= F_{d} Q_{free} where Q_{free} is defined as in Mode 2  Free Weir Flow Equation, and the drowning factor F_{d}_{ }is given by: F_{d} =√ [(1  (y_{2 } z_{cup})/(y_{1} z_{cup})) / (1  m)] or F_{d} = (1  (y_{2 } z_{cup})/(y_{1} z_{cup}))/ (0.3* (1  m)), if the first formula for the drowning factor gives F_{d} < 0.3 where: Q_{drowned} is the discharge, y_{1} is the upstream water elevation above the invert, y_{2 }is the downstream water elevation above the invert, z_{cup }is the level of the sill on the upstream side of the structure, z_{inv }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. 
Mode 4  Orifice flow
Condition  y_{1}  z_{inv}_{ }> 1.5h or y_{2}  z_{inv} > h (rectangular) y_{1}  z_{inv}_{ }> 1.25d or y_{2}  z_{inv} > d (circular) 
Equation  Q_{ori}_{ }= C_{d}_{ }C_{full}_{ }A √ (2g Δh) or for inverted syphons: Q = min (Q_{free}_{,} Q_{ori}) where Q_{free} is defined as in Mode 2  Free Weir Flow Equation, and Q_{ori}_{ }is defined as in Mode 4  Orifice flow where: Q_{ori} is the discharge, y_{1} is the upstream water elevation above the invert, y_{2} is the downstream water elevation above the invert, z_{inv} 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(y_{1}  y_{2} , y_{1}  0.8h) (rectangular hole), Δh = min(y_{1}  y_{2} , y_{1}  0.5d) (circular hole), C_{d} is the fixed discharge coefficient for surcharged flow given by C_{d} = 0.799 for a rectangular hole or C_{d} = 0.6 for a circular hole, and C_{full }is the specified surcharged (orificetype) flow calibration factor, default = 1.0. Note: the coefficient used within the equation is the product of the (fixed) value C_{d} and the (userentered) value C_{full}. If you require a different coefficient, adjust the calibration factor (C_{full}) accordingly, for example a rectangle with rounded corners can be modelled using a calibration factor between 0.75 and 1.0. 
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 F_{d} 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 F_{d} = 0.3 and F_{d} = 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  z_{inv}, z_{soff}, Area, z_{cup}, z_{cdn}, shape
Line 5  C_{weir}, C_{full}, m
Examples of the datafile format are given below.