07/06/2016 11:31:12

*By Konrad Adams, Senior Developer - Flood Modeller, Jacobs*

### Introduction

One of the regular sets of questions asked to the Flood Modeller Support Team relate to the blockage unit – “how is it connected?”, “what do all the five node labels mean?” and “what calculations does it actually use?”.

Many flooding incidents are caused or exacerbated by blockages in the watercourse, typically at the entrance to bridges or culverts. Modelling flood events with varying degrees of blockages at critical locations can help inform maintenance and incident response decision making.

The Flood Modeller blockage unit can effectively model a single or a number of blockage scenarios for this purpose. The blockage proportion may vary with time. The increase in upstream water level is calculated using the Bernoulli equation to derive the head loss. Put simply, ∆h=kv^2/2g.

### Model Connectivity

One of the frequently asked questions is about connectivity. With flexibility comes a degree of complexity, and we have potentially five node labels to select. The first two are connection labels and the remaining three are reference sections (see later) and not always necessary (although it is recommended to include these for clarity).

The first thing to note is that the blockage is treated as a structure in its own right. Therefore it has two **connection** node labels (**label #1 **and** label #2** for the upstream and downstream nodes, respectively). As with any structure, the node label #1 of the blockage is connected to the channel section, junction or other structure *immediately* upstream of it. Conversely, node label #2 of the blockage (which must be different from label #1) is connected to the channel section, junction or other structure *immediately* downstream of it.

*General Flood Modeller 1D connectivity rule: each structure node label must appear exactly twice in a model network (excluding any reference/remote nodes).*

So that’s the **connectivity** node labels sorted. Now for the remote or reference nodes (**labels 3-5**). Note that these do not affect connectivity in the model – they just tell the model where to obtain velocities from. Because the blockage unit needs a velocity for the Bernoulli equation, it needs a wetted area (v=Q/A) and for that it needs a cross section – from a river, conduit or bridge unit. Put simply, label 3 needs to be the most appropriate, perhaps nearest, section upstream and label 4 the same downstream. Indeed, if label 1 is a river/conduit/bridge unit, then it makes sense for label 3 to be the same as label 1. I stress again that this does not mean the blockage unit is physically connected to labels 3 and 4.

Similarly, **node label 5** needs to be a river, conduit or bridge unit and represents the section to be constricted. Typically, this will be the bridge or conduit section immediately downstream of the blockage, and is generally the same as label 4.

In the schematisation below, the blockage is representing a blockage at a culvert (modelled using CONDUIT units), and is therefore placed between the open channel and the culvert (in this case upstream of the culvert inlet loss unit).

Therefore, the upstream reference section is the river section upstream, i.e. same as the connectivity label, label #1 (EW01.023) in this case.

The downstream reference section is the first CONDUIT node (EW01.023c). Note this is different from the downstream connectivity node (label #2) since there is a CULVERT INLET loss between the blockage and the CONDUIT (the reference section must contain cross-sectional information).

The constriction reference section (label #5) in this case is also the first CONDUIT node (EW01.023c).

### Usage

The headloss due to the blockage, *Δh*, is derived from the Bernoulli equation representing both a contraction and an expansion, as follows:

where:

K_{1 = }Inlet/upstream loss coefficient

K_{2 = }Outlet/downstream loss coefficient

P = Blockage proportion

V_{3} = Velocity at label 3, the upstream section

V_{4 }= Velocity at label 4, the downstream section

V_{5} = Velocity at label 5, the section to be obstructed

Note that:

*V*is calculated using the area of section 3 at the upstream water level (WL at node 1);_{3}*V*is calculated using the area of section 4 at the downstream water level (WL at node 2);_{4}*V*is calculated using the area of section 5 at the upstream water level (WL at node 1)._{5 }- The discharge – used to calculate velocity via v=Q/A – is the same at both node labels (mass is conserved and there is no storage in the unit).

Note that you can specify a time-varying blockage proportion, p, or use a constant value. A value of p=0 indicates no blockage; a value approaching 1 would indicate a 100% blockage (p must be strictly less than 1).

If a Bridge unit is being used as a reference section, the area used to derive velocity is the wetted area of the bridge *opening*.

Note: If the upstream and constriction sections differ, there will be a contraction loss even for a zero blockage (with reference to the first term on the right-hand side of the equation, the areas, and hence velocities will be different). Thus the blockage unit can model a pure contraction (or conversely expansion) loss. Alternatively, to prevent this, e.g. if the contraction loss is already accounted for elsewhere, one should set the upstream loss coefficient, K_{1}, to zero.

For instance in the example above, a blockage is placed in front of the culvert inlet. In this instance, one would be advised to set the K_{1} coefficient to zero, i.e. to prevent double counting the headloss.

When using a Culvert Inlet unit, one could alternatively apply a blockage to a trash screen, which behaves in a similar manner, instead of using a blockage unit. A significant difference is that the blockage proportion in the Culvert Inlet unit is fixed, and not time-varying.

### Examples

Note that the following examples all relate to culverts; for the entry and exit blockage examples, the culvert unit could equivalently be replaced by a bridge, in which case the conduit reference section would be replaced by the appropriate bridge section.

### Obstruction at the entrance to a culvert

The upstream and downstream sections are different. The user should set the constriction section to be the **downstream** section, and we have:

### Obstruction in a river section or culvert

Here, the upstream and downstream sections are the same. The constriction section should be the downstream section, K_{1} should be used to specify the inlet loss and K_{2} the outlet loss. The equations become:

### Obstruction at the exit from a culvert

The upstream and downstream sections are different. The user should set the constriction section to be the **upstream** section, and we have:

### Notes

If including both a contraction and expansion loss, a typical value for the upstream loss coefficient K_{1} would be 0.5, and the downstream loss coefficient K_{2} would be 1.

The blockage is modelled as a vertical blockage, i.e. the blockage *proportion* does not vary with depth.

Blockage units can be used in event data files – this means one can model several different scenarios, e.g. different proportions or different time-profiles using the same model network.