Symmetrical Conduit
• 21 Oct 2022
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# Symmetrical Conduit

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Article Summary

The Symmetrical Conduit models closed-topped symmetrical conduits or culverts of irregular section. If the conduit to be modelled is not of rectangular, circular, full arch, or sprung arch type then the Symmetrical Conduit should be used. A minimum of two Symmetrical conduits is required, one for each end of the conduit reach.

## Data

Field in Data Entry Form

Description

Name in Datafile

Section Label

section label

label1

Distance to Next Conduit

distance to next section (m)

dx

n/a

number of cross-section data points

ndat

X Coordinate

x co-ordinate of i'th point (x = 0 at centre line) (m)

x(i)

Y Coordinate

y co-ordinate (ie level) of i'th point (m AD)

y(i)

Friction Coefficient

Colebrook-White friction coefficient between (i-1)th and i'th point (in units of metres)

ks(i)

## Theory and Guidance

The Symmetrical Conduit models closed topped symmetrical conduits/culverts of irregular section in either free surface or pressurised flow mode. If the conduit to be modelled is not of rectangular, circular, full arch, or sprung arch type then the Symmetrical Conduit should be used. The Symmetrical Conduit always uses the Colebrook-White form of friction equation.

The data points must be entered in an anti-clockwise sense starting at the invert centre line - ie only the right half is entered. Note that ks must be input in metres.

A minimum of two Symmetrical Conduits is required, one for each end of the conduit reach. Intermediate cross sections can be specified by additional Symmetrical Conduits or by using Replicated Sections. Unlike other conduit types, you can use Interpolated Sections between Symmetrical Conduits.

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 an Orifice would be preferable in many cases since it specifically models orifice flow.

The Symmetrical 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, such 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 in the Symmetrical Conduit are the mass conservation or continuity equation: (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: (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 Symmetrical 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

Symmetrical 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]

Line 2 - keyword `SECTION'

Line 3 - label 1

Line 4 - dx

Line 5 - ndat

Line 6 - x(i), y(i), ks(i)

Line 6 is repeated for all data points

Line 1 to Line 6 + ndat are repeated n times, one for each distance step. A dx value of zero signifies the end of a conduit "reach". 