Preissmann Slot Theory

The Sprung Arch Conduit models sprung arch section conduits. A minimum of two Sprung Arch conduits are required, one for each end of the conduit.

• Preissmann Slot Theory Definition
• Preissmann Slot Theory Game
• Preissmann Slot Theory Games

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).
• 45 Consequently, the results show (1) that the Preissmann slot needs to be chosen appropriately small and (2) that neglecting the influence of the Preissmann slot width on model results needs to be verified for a specific model setup by a sensitivity analysis. Accordingly, the Preissmann slot width is set to 0.0001 m for subsequent model runs.

Theory and Guidance

The Sprung Arch Conduit models sprung arch section conduits. A minimum of two Sprung Arch Conduits are required, one for each end of the conduit. Intermediate cross sections can be specified by additional Sprung Arch Conduits or by using Replicated Sections.

The width and height values 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.

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. On the premise of water hammer theory, a numerical model is proposed for simulating the filling process in an initially empty water conveyance pipeline with an undulating profile. Assuming that the pipeline remains full and ignoring air and water interactions in the already filled pipeline, the ongoing filling is simulated using the method of.

The Sprung 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, such that the water level calculated by the program is the piezometric level. This means that the cross-sectional area and conveyance remain 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 Sprung Arch Conduit are the mass conservation or continuity equation:

Preissmann Slot Theory Definition

and the momentum conservation or dynamic equation:

General

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

Sprung Arch 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 `SPRUNGARCH'

Line 3 - label 1

Line 4 - dx

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

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

Line 7 - fribot, frisid, friarc

Lines 1 to 7 are repeated n times, one for each distance step. A dx value of zero signifies the end of the conduit 'reach'.

Note for SWMM6 – this may be useful for any discussion of a Slot in SWMM6. A Preissmann Slot is used in InfoWorks ICM, XPSWMM and one of the solutions of SWMM4

Wave Speed

The wave speed, c, is influenced by the elasticity of the pipe wall. For a pipe system with some degree of axial restraint a good approximation for the wave propagation speed is obtained using

where Ef = elastic modulus of the fluid (for water, 2.19 GN/m2, 0.05 Glb/ft2)

ρ = density of the fluid (for water, 998 kg/m3, 1.94 slug/ft3)

Ec = elastic modulus of the conduit (GN/m2, Glb/ft2)

D = pipe diameter (mm, inch)

t = pipe thickness (mm, inch)

KR = coefficient of restraint for longitudinal pipe movement.

Preissmann Slot Theory Game

The constant KR takes into account the type of support provided for the pipeline. Typically, three cases are recognized with KR defined for each as follows (m is the Poisson’s ratio for the pipe material):

Preissmann Slot Theory Games

Case a: The pipeline is anchored at the upstream end only.

KR = 1 – m / 2

Case b: The pipeline is anchored against longitudinal movement.

KR = 1 – m2

Case c: The pipeline has expansion joints throughout.

KR = 1

The following table provides physical properties of common pipe materials.

Table 3-8: Physical Properties of Common Pipe Materials