 23 Oct 2022
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Circular Conduit
 Updated on 23 Oct 2022
 4 Minutes to read

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The Circular Conduit is used to model a closed conduit, or culvert, where the cross section is circular. The cross section is specified by the invert level and diameter. A minimum of two Circular Conduits are required, one for each end of the conduit.
Data
Field in Data Entry Form  Description  Name in Datafile 

Section Label  Section label  Label1 
Distance to Next Conduit  Distance to next section downstream (m)  dx 
Equation  Form of friction equation to be used  keyword MANNING or COLEBROOKWHITE  frform 
Elevation of Invert  Invert level (m AD)  inv 
Diameter of Conduit  Diameter of conduit (m)  dia 
Friction Below Axis  Friction below axis level (in units of metres for ColebrookWhite)  fribot 
Friction Above Axis  Friction above axis level (in units of metres for ColebrookWhite)  fritop 
Use Bottom Slot  Choose whether to include a bottom slot or to use the model default (global) (bslot='ON', 'OFF' or 'GLOBAL'(default).  bslot 
Distance of slot top  Height of the top of the bottom slot with respect to the culvert invert (m). If zero, the default value will be used; if negative, the global value will be used.  dh 
Total Depth of Bottom Slot  Total depth of the bottom slot (m). If zero, the default value will be used; if negative, the global value will be used  dslot 
Use Top Slot  Choose whether to include a top slot or to use the model default (global) (tslot = 'ON', 'OFF' or 'GLOBAL' (default).  tslot 
Distance of slot bottom  Depth of the bottom of the top slot relative to the culvert soffit (m). If zero, the default value will be used; if negative, the global value will be used.  dh_top 
Total Height of Top Slot  Total height of the top slot (m). If zero, the default value will be used; if negative, the global value will be used  hslot 
Theory and Guidance
The Circular Conduit is used to model a closed conduit, or culvert, where the cross section is circular, in either free or pressurised flow modes. The cross section is specified by the invert level and diameter. Two friction sectors are specified for the lower and upper halves of the cross section.
A minimum of two Circular Conduits are required, one for each end of the conduit. Intermediate crosssections can be specified by additional Circular Conduits or by using Replicated Sections. All conduits in a reach must have the same crosssectional shape, so you shouldn't mix Circular Conduits with other conduit types.
The diameter may change between sections, although the PseudoTimestepping Method will have to be used for steady state simulations, as the Direct Method cannot solve for this situation. This is also true for friction values that vary along the conduit reach.
Both free surface and pressurised flows are allowed. The pressurised flow approach is particularly appropriate for hydraulically long culverts, but may not be suitable in situations which approximate to orifice flow in a short culvert. A general alternative for short culverts is the Bernoulli Loss, but the Orifice would be preferable in many cases since it specifically models orifice flow.
The Circular Conduit is based on the St Venant equations which express the conservation of mass and momentum of the water body. Pressurised flow is accommodated through incorporation of an infinitesimally thin frictionless slot in the top of the conduit, known as a Preissmann Slot, so that the water level calculated by the program is the piezometric level. This means that the crosssectional area and conveyance remains unaltered if the water level rises above the soffit level.
Localised regions of supercritical flow can be modelled approximately.
Equations
The equations used for the Circular Conduit are the mass conservation or continuity equation:

where: Q = flow (m^{3}/s) A = cross section area (m^{2}) q = lateral inflow (m^{3}/s/m) x = longitudinal channel distance (m) t = time (s) 
and the momentum conservation or dynamic equation:

where: h = water surface elevation above datum (m) ß = momentum correction coefficient g = gravitational acceleration (m/s^{2}) k = channel conveyance. Channel conveyance can be calculated using Manning's equation or the Colebrook White equation. See Conduit Channel Conveyance. 
General
Steep sloping conduits will need closer cross section spacing than mild sloping culverts.
Exit and entry losses (and any abrupt intermediate contractions or expansions) are not covered by the Circular Conduit and may be included explicitly using the Culvert Inlet and Culvert Outlet or Bernoulli Loss, for example.
Critical depth control at entry or exit and entrance geometry control are not included. These flow modes can be approximated by inclusion of some sort of Weir at entry or exit or by use of an Orifice at the entrance (or an orifice alone for a hydraulically short culvert).
Connectivity Rules
Circular Conduits should not be connected directly to:
 different Conduit types (with different cross sectional shape)
 any River types
 Interpolated Sections
You can connect different types of reach using a Junction if no head loss occurs at the join. Alternatively, the specialised Culvert Inlet and Culvert Outlet can be used to model the losses associated with transitions from open channel to culverts and vice versa. Bernoulli Losses are also available to model more generalised losses.
Datafile Format
Line 1  keyword CONDUIT'[comment]
Line 2  keyword CIRCULAR'
Line 3  Label1
Line 4  dx
Line 5  frform
Line 6  inv, dia, bslot, dh, dslot, tslot, dh_top, hslot
Line 7  fribot, fritop
Lines 1 to 7  repeated n times, one for each distance step. A dx value of zero signifies the end of the conduit "reach".