FIX WATER DEPTH AS THE END POINT OF DRAIN

TYPES OF OUTFALL BOUNDARY CONDITION #

One of the most important components in any network are the outfall boundary conditions. In MiTS3, you can have outfalls that are Free, Normal and Fix.

We will examine the fixed outfall condition and compare the reported software depths with a manual calculation.

A simple MiTS model was created consisting of a single catchment generating inflow to a conduit, which then discharges to a terminal node with a fixed outfall level. The model was analysed using Dynamic Wave routing.

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Information

Major Design Storm ARI: 50 years

FIX OUTFALL CONDITION ANALYSIS RESULT #

Constant Water Depth #

Water depth and Water depth/drain ratio of drain in a fix outfall condition (MiTS UI)

Drain Flow and Water depth in a fix outfall condition (Export to spreadsheet)

Result and Discussion #

Based on the simulation depicted above, there are three phases occurring:

1. Rainfall Event: 0 – 60 minutes

At the start of the simulation, the reported conduit depth is about 0.25 m. This is a link result; the fixed outfall water-surface elevation is 28.50 m. We will distinguish these quantities in the manual check below. From 0 to 30 minutes, the flow in the conduit increases from 0 to approximately 1.50 m³/s. Water depth increases from about 0.25 m to 0.46 m. From 30 to 60 minutes (where the peak rainfall period is occurring), the drain flow and water depth remain approximately constant.

2. Catchment draining: 60 – 90 minutes

After the storm ends at 60 minutes, the flow gradually decreases. By around 90 minutes, the reported flow is almost zero. This is consistent with the runoff recession in this example; rainfall ending at 60 minutes does not mean runoff stops immediately.

3. After 90 minutes: Why is water depth still at 0.25 m even though rainfall has already stopped?

This is the important observation when we introduce a fixed outfall. The fixed outfall is imposing a downstream water level. The tailwater and backwater derivation explains how a known downstream level enters the steady energy balance for upstream water levels. After about 90 minutes, the reported flow is nearly zero, but the downstream part of the conduit remains wet. The plotted 0.25 m link depth needs the reporting interpretation developed below.

Think of a pipe discharging into a lake. After the rain stops and no more water is flowing through the drain/ pipe conduit, the lake level stays the same, so water remains in the downstream part of the pipe instead of draining out completely.  

Manual calculation after the flow stops #

The tailwater article relates the upstream and downstream water levels through velocity heads and losses. Once the water is at rest, velocity and flow-related losses vanish. The water surface in the part of the drain connected to the receiving water is therefore level at 28.50\;\text{m} .

Let z_b be the local drain invert elevation and y the water depth, both in metres. Where the invert lies below that surface, y=28.50-z_b . Where it lies above the surface, the drain is dry. Combining both cases gives

\displaystyle y=\max(0,\,28.50-z_b).

At the outlet, the manual depth is y_d=28.50-28.00=0.50\;\text{m} . At the upstream end, the invert is 0.50\;\text{m} above the receiving water, so y_u=0 . A negative result from 28.50-29.00 means the water does not reach that bed; it is not a negative water depth.

The software graph reports about 0.25\;\text{m} for the link. This agrees with the average of the two endpoint depths:

\displaystyle y_{link}\approx\frac{y_u+y_d}{2}=\frac{0+0.50}{2}=0.25\;\text{m}.

Here y_{link} is the reported link depth, distinct from either endpoint depth. It should not be read as the exact physical depth halfway along the drain. For a straight invert falling uniformly from 29.00 m to 28.00 m, the halfway invert is 28.50 m, exactly where the static water meets the bed.

The agreement explains the residual link depth. It does not establish that 0.25 m is the depth everywhere, or independently validate the complete storm simulation.

Backwater effect (Tailwater level is higher than Headwater level) #

 When a drain discharges into a river or pond, a high receiving-water level can hold water back and raise the upstream level, even while water continues to flow downstream. The tailwater and backwater article explains how the downstream level, flow velocity and energy losses determine the upstream water level. If the receiving-water level rises above the water level in the connected storage, water can also flow back through the outlet into the storage.

The following model illustrates this reverse flow. A storage facility connects to an outlet drain with an invert elevation of 27.00 m, while the receiving-water level is fixed at 28.00 m. We use Dynamic Wave routing to follow the outlet flow as runoff enters the storage and its water level rises.

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Information

Result and Discussion #

The fixed tailwater of 28.00 m affects how readily the storage can empty. For a given storage water level, a higher tailwater leaves less head available to drive water through the outlet. If the outlet cannot pass runoff as quickly as it arrives, water accumulates and the storage depth increases. As developed in the tailwater article, passing the same steady discharge against a higher downstream level requires a higher upstream water level, with velocities and losses accounted for.

The circled part of the graph shows a further effect: the outlet flow is negative while the storage level rises. Receiving water is entering through the outlet and adding to the water already stored. Tailwater therefore affects storage in two ways: it can restrict discharge, and it can supply additional water through backflow. Both can leave less storage capacity available for incoming runoff.

When the outlet flow becomes positive, the storage is discharging again, but it still discharges against the same 28.00 m tailwater. The storage can continue to fill if runoff enters faster than water leaves.

CONCLUSION #

A fixed outfall specifies a receiving-water elevation. In the no-flow example, 28.50 m tailwater above a 28.00 m outlet invert gives 0.50 m depth at the outlet. The reported link depth of about 0.25 m is consistent with averaging a dry upstream end and the wet downstream end; it is not a uniform depth along the conduit.

The manual check explains the remaining water after flow stops. Dynamic Wave routing also follows changing inflow, storage and flow reversal during the storm. For reverse flow, compare the hydraulic heads on the two sides; tailwater depth above the outlet invert alone does not give the driving head.