Preissmann Slot Theory
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
According to the Preissmann slot model, pressurized flow can be equally calculated through the free-surface equations by adding a conceptual slot at the top of a closed pipe (Figure 1b). A 'Priessmann slot' technique for linking open channel and surcharged flow is used exclusively by the model. Warning messages concerning gaps between conduits at a node were eliminated. Special conditions accounted for are surcharged closed conduits, overtopping open channels, and rectangular culvert calculations for wetted perimeter.
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 COLEBROOK-WHITE | 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 Colebrook-White) | fribot |
Friction Above Axis | Friction above axis level (in units of metres for Colebrook-White) | 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 cross-sections can be specified by additional Circular Conduits or by using Replicated Sections. All conduits in a reach must have the same cross sectional shape, so you shouldn't mix Circular Conduits with other conduit types.
The diameter may change between sections, although the Pseudo-Timestepping 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 cross-sectional 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 (m3/s) A = cross section area (m2) q = lateral inflow (m3/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/s2) 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
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]
Preissmann Slot Theory Definition
Line 2 - keyword `CIRCULAR'
Line 3 - Label1
Line 4 - dx
Preissmann Slot Theory Game
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'.