Circular Conduit
  • 23 Oct 2022
  • 4 Minutes to read
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Circular Conduit

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Article Summary

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 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:

 

mass_conservation(1)

(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(1)

(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

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:

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".

RiverNodesimagesCircularConData.gif


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