Full Arch Conduit

23 Oct 2022
4 Minutes to read

Full Arch Conduit

Updated on 23 Oct 2022
4 Minutes to read

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The Full Arch Conduit models a closed conduit, or culvert, where the cross section is a full arch with a horizontal invert. A minimum of two Full Arch 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
Elevation of Invert	invert level (m AD)	inv
Width	width at invert level (m)	width
Height	height of crown above invert (m)	archyt
Equation	form of friction equation to be used (Mannings or Colebrook-White)	frform
Value on Invert	friction coefficient along invert (in units of metres if the Colebrook-White equation is used)	fribot
Value on Arch	friction coefficient of arch (in units of metres if the Colebrook-White equation is used)	friarc
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
Top 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 Full Arch Conduit models a closed conduit, or culvert, where the cross section is a full arch with a horizontal invert, in both free and pressurised flow modes.

The cross section is specified by the invert level, the width of the base (diameter) and the height from invert to crown. As the cross-section shape is assumed to be part of a circle, the height of the crown can never be more than half of the width of the base.

A minimum of two Full Arch Conduits are required, one for each end of the conduit. Intermediate cross sections can be specified by additional Full Arch Conduits or by using Replicated Sections. All conduits in a reach must have the same cross sectional shape, so you shouldn't mix Full Arch Conduits with other conduit types.

The width and height 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 hydraulically short culverts is the Bernoulli Loss, but an Orifice would be preferable in many cases since it specifically models orifice flow.

The Full Arch 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 software 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 in the Full Arch Conduit are the mass conservation or continuity equation:

mass_conservation(2)

(1)

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:

momentum_conservation(2)

(2)

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

Exit and entry losses (and any abrupt intermediate contractions or expansions) are not covered by the Full Arch 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

Full Arch 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 FULLARCH

Line 3 - label 1

Line 4 - dx

Line 5 - frform - keyword 'MANNING' or 'COLEBROOK-WHITE'

Line 6 - inv, width, archyt, bslot, dh, dslot, tslot, dh_top, hslot

Line 7 - fribot, friarc

Lines 1 to 7 - repeated n times, one for each distance step; a dx value of zero signifies the end of the conduit "reach".

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What's Next

Rectangular Conduit

Table of contents

Data
Theory and Guidance
Datafile Format