Asymmetrical Conduit
• 15 Aug 2022
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# Asymmetrical Conduit

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The Asymmetrical Conduit models closed-topped conduits of any possible shape of cross-section. If the conduit to be modelled is not of rectangular, circular, full arch, sprung arch or any other Symmetrical shape, then the Asymmetric Conduit should be used. A minimum of two Asymmetrical conduits are required to create a conduit reach.

## Data

Field in Data Entry Form

Description

Name in Datafile

Section Label

Section label – identifier

Label1

Distance to next conduit

Distance to next conduit section

dx

n/a

Number of cross-section data points

Not a data entry - solver sets this based on number of x-y data rows defined

ndat

x-coordinate

x-coordinate of the i-th point of the section

Recommendation: Define x-y coordinates in an anti-clockwise direction

x(i)

y-coordinate

y-coordinate of the i-th point of the section

Recommendation: Define x-y coordinates in an anti-clockwise direction

y(i)

Friction coefficient

Manning’s or Colebrook-White’s friction coefficient between (i-1)-th and i-th point of the section (entry must be greater than zero)

ks(i)

Friction Method

Identifier for choosing between Manning’s and Colebrook-White friction law. If method is given as MANNING, the Manning's friction law will be applied; if method is given as DARCY the D'Arcy equation will be used with the Colebrook-White friction factor.

If method is blank or given as anything other than MANNING or DARCY, a warning is given by the software and the D'Arcy equation with Colebrook-White friction factor is implemented by default.

method

## Theory and Guidance

The Asymmetrical Conduit models closed topped conduits/culverts of any possible shape of cross-section in either free surface or pressurised flow mode. If the conduit to be modelled is not of rectangular, circular, full arch, sprung arch or any Symmetric shape, then the Asymmetrical Conduit should be used. The Asymmetrical Conduit gives the option to either use the Colebrook-White form of friction equation of the Manning’s one.

The data points must be entered in an anti-clockwise sense without limitations on the location of the starting point. Care should be taken as not to create a self-intersecting shape.

A minimum of two Asymmetrical Conduits is required, one for each end of the conduit reach. Intermediate cross-sections can be specified by additional Asymmetrical Conduits or by using Replicated Sections. Please note that Interpolate sections cannot be used.

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 Asymmetrical 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 Asymmetrical 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 Asymmetrical 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 and Data Entry 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 reaches 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.

It is recommended that your cross-sectional (x, y) data points are provided in an anti-clockwise direction as this is a requirement of the solver. However, the solver will attempt to reverse the direction if it finds points defined in a clockwise direction. The resulting shape defined by your data points should not contain self-intersections. Therefore, take care entering data in the correct order and always check your final shape by using the plot function in the interface.

Note
The solver will automatically join the last point entered back to the first point to close the shape.

Each data point entry also requires a friction coefficient (Mannings or Colebrook-White).

Note
The default friction law in the interface is the Colebrook-White formula.

Figure 1: Example of a conduit section made of an irregular bed shape capped by a man-made lid. The dots represent the (x,y) coordinates pairs to input. The conduit shown is on free surface mode with water stage at 5.7 mAD.

## Datafile Format

The following format is proposed for the input of data written in .dat file:

Line 1 - keyword ‘CONDUIT’

Line 2 - keyword ‘ASYMMETRIC’

Line 3 - label1

Line 4 - dx, method

Line 5 - ndat

Line 6 to 6+ndat - x(i), y(i), ks(i)