# Modeling Reference - Discharge To Atmosphere

 Product(s): HAMMER Version(s): CONNECT Edition, V8i Area: Modeling

# Overview

This TechNote explains how the Discharge to Atmosphere (D2A) element works and its typical application in transient simulations in HAMMER. The example model file at the end of the TechNote can also be found the Samples folder of the HAMMER installation file (C:\Program Files (x86)\Bentley\HAMMER\Samples).

# How it Works

The Discharge to Atmosphere element can be used to model a valve to discharging to atmosphere, orifice to discharging to atmosphere, and head vs. flow rating tables. It is used to model an opening or orifice that allows flow to leave the pipe network and discharge to the atmosphere. You can model it as a fixed orifice that is always open, or a valve that is either initially open or closed, then opens or closes during the transient simulation. It can be placed in series with the main water line or at a "T," as shown below.

`Note: It is important to understand that this element discharges to atmosphere, not between the adjacent pipes. So in the above case of an in-line orientation, flow still passes through the pipeline beneath the valve, regardless of if the valve is opened or closed.  `

In the calculation engine, it is modeled as a demand point located a hydraulically short distance from its node coordinates, based on the wave speeds of the pipes connected to it. The initial pressure and flow entered by the user are used to automatically calculate an emitter coefficient for the orifice. This is the term CA in the orifice equation below.In turn, this will be used during the simulation to calculate transient outflows as the pressure changes. This applies to both the initial conditions solver as well as the transient solver. HAMMER uses the coefficient CA to calculate other flows and their corresponding pressure drop.

Here is the orifice equation used for the D2A in HAMMER:

Q = C A (2 g P)^0.5

Q - Discharge (cfs, cms)
C - A 'discharge coefficient' (distinct from CV used elsewhere in HAMMER) which will be computed based on the typical flow/pressure
A - The cross-sectional area of the opening (ft, m) - this is combined with the "C" as a single term
g - gravitational acceleration
P - Pressure head (ft, m)

As you can see, once the "CA" is calculated from the initial head/flow, HAMMER can solve for other flows, as the pressure head changes during the simulation.

### Example:

Here is an example, where the "Pressure Drop (Typical)" is set to 1 m and the "Flow (Typical)" is set to 0.5 m^3/s  :

Q = CA (2*g*P)^0.5
0.5 = CA (19.6)^0.5
0.5 = CA * 4.4272
CA = 0.1129

If the pressure at the D2A is 1 m, then the outflow is exactly 0.5 m^3/s:

Now, say the pressure changes from 1 m to 10 m:

Q = CA (2*g*P)^0.5
Q = (0.1129) * (2*g*10)^0.5
Q = (0.1129) * 196^0.5
Q = 1.58 m^3/s

This is the flow you see in HAMMER when the pressure in the model is 10 m:

## Air Pocket Formation

If the pressure drops below zero (sub-atmospheric) at the D2A element during the transient simulation, the D2A allows air into the system. When this happens, the air enters the pipeline freely on the assumption that the opening for the liquid is infinite for air. In this case, the node acts like a reservoir at zero pressure and the air pocket respectively expands or contracts accordingly as the liquid flows away from or towards the node, but the air remains at the branch end point(s) located at the D2A. The rate of change of the air volume is based on the water flow rate of the adjacent water column in the pipe. If a check valve further upstream is closed, such as in an upstream pump station at a lower elevation, you may not see any air enter because the water column will not be able to move backwards (or may only be able to move slightly due to the  elasticity of the water column). Similar to an air valve, the admittance of air from a D2A will only be able to help protect the system in the immediate vicinity of the D2A; pressure can still drop further upstream. See below for details on the application of a D2A for simulating an "inrush" or pipe filling/emptying.

For more information on the assumptions related to tracking air/vapor pockets in a transient simulation, see the following link: Assumptions and limitations of tracking air or vapor pockets in HAMMER.

# When to Use it

### Common applications of the D2A acting as a valve

1. Opening or closing of a hydrant, blowoff, sprinkler or other discharge - Select "Valve" as the Discharge Element Type and specify the initial status. If the valve is initially closed at the start of the transient simulation, it will open and vice versa. Set the Time to Start Operating and the Time to Fully Open or Close; the valve opening increases linearly. Set the emitter value for the element by specifying the Pressure Drop (Typical) at some flow rate ("Flow (Typical)"). See this link for further details: Transient simulation for a hydrant closure or opening.
2. Modeling a main break - The Discharge Element Type is also "Valve" in this case, but the "Time to Fully Open or Close" would be set to zero. This is because it is conservative to model the rupture occurring quickly and producing a large opening. Essentially the initial conditions describe the normal pipe and appropriately conservative flow conditions just before the break, then the transient simulation instantly opens the 'valve' to initiate transition to a ruptured condition. To represent the size of the opening, it is recommended that the user set the "Pressure Drop (Typical)" to the steady-state pressure (observed prior to the break), and only vary the "Flow (Typical)" according to the equation found in the "Any free discharge point" section below.
A sensitivity analysis wherein the cross sectional area, A, is varied would illustrate the consequences of a range of breaks, with an upper limit to A being the diameter of the incoming pipe(s). The analysis should also consider different locations of the break(s). Depending on the pipe network's topology, a sudden break can lead to the formation of vapor pockets with ensuing collapses and pressure spikes.

### Common applications of the D2A acting as an Orifice

1. Demand/consumption points that can let air in - In HAMMER, any demand at a junction or hydrant is called a consumption node and is treated as an orifice discharging to atmosphere that cannot allow air back into the system during periods of subatmospheric pressure. This is because the majority of demands entered into hydraulic models are really the sum of several houses or demand points, each located at a significant distance from the point where their aggregate demand is being modeled. HAMMER assumes that any air allowed into the system at the individual demand points cannot reach the aggregate demand location. If this is not the case, you must model the demand using the Discharge To Atmosphere element, set as an orifice. This is because upon subatmospheric pressure, the discharge to atmosphere element allows air into the system.
2. Any free discharge point - For example, the end of a sewer force main that discharges to an unsubmerged manhole, or a free discharge into the top of of a top-fill tank. You would need to decide how to compute the headloss through the pipe outlet (and thus the corresponding "Flow (Typical)" and "Pressure Drop (Typical"), but a decent estimate would be to use the standard headloss equation: headloss = k*v2/2g, where k is set to 1, v is the flow velocity and g is the acceleration due to gravity. Alternatively, if the outlet orifice is smaller than the pipe diameter, you could use the orifice equation, V = C*(2g*headloss)0.5 These equations are very similar to each other, and in either case, the headloss is essentially the pressure drop. So, the workflow to find the typical flow and typical pressure drop would be to select an approximate flow (and therefore velocity) and use one of the above approaches to solve for an appropriate "Pressure drop (Typical)". In order to do this, you would need to estimate a value for C. There is some documentation available for reference for such estimates. For instance, Brater and King (1976) lists orifice coefficients for various heads and sizes of circular, square, rectangular, and triangular shapes, and the U.S. Soil Conservation Service (1986) provides a chart of orifice coefficients for orifice plates placed over pipe opening.

As an example, assume a case where you know the flow but not the pressure or head. In this case, the flow is 10 cfs through a 12 inch opening. The velocity in this case would be: V = Q/A = 10 / (pi*0.5^2) = 12.73 ft/s. If you assume C = 0.6, you could calculate the corresponding appropriate headloss using the orifice equation relationship: = (V/C)^2 / 2g = (12.73 / 0.6)^2 / (2 * 32.174) = 7 ft. In this example, the "Pressure Drop (Typical)" would be set as 7 ft H2O. HAMMER would then use the orifice equation to compute a change in outflow as the pressure changes. If you already know the flow at a corresponding head, you would simply enter them in the D2A properties and HAMMER will calculate the discharge coefficient internally and use that during the transient simulation to vary outflow with pressure.

3. Transients initiated by an 'inrush' event - When a pump turns back on in a sewer force main, it may expel some air from the downstream end. The headloss through the discharge opening causes a resistance that can result in a severe upsurge once the water column reaches the opening. For example, with a small orifice size, an upsurge occurs when the flow reaches it because the water cannot get out of the pipe fast enough. Modeling this situation can be done by using the Discharge to Atmosphere element operating as an orifice. The initial conditions must describe the low head condition (zero pressure at the discharge to atmosphere element) and you must enter a volume of air in the "Gas Volume (initial)" field. You would then have the head increase during the transient simulation (pump turning on or periodic head element with head value increasing, for example.) The "Flow (Typical)" and "Pressure Drop (Typical)" would be estimated similar to item 2 above. The higher the "Pressure Drop (Typical)," the smaller the orifice size and the more resistance to flow, resulting in a higher upsurge after the air pocket is expelled. See further above for details and assumptions about air pockets. For more information, see the following link: Modeling the filling of an empty pipe in HAMMER.

Note: The "Gas Volume (Initial)" will impact the timing of the release of the air. The value you enter will be up to your engineering judgment, but a good starting point may be the volume of the empty pipe. A larger volume of air for the same size orifice will take longer to be expelled from the D2A. This, in turn, will impact the head increase at the source. The most important impact on the system will occur with the air is fully expelled, which is when the transient would occur. So while a large air volume will take longer to expel, the setup and size of the D2A may prove to the be most important part of the transient event.

4. Impulse turbine - The turbine element in HAMMER is not used to represent impulse turbines. Transients caused by impulse turbines can be approximated in HAMMER by using a Throttle Control Valve (TCV) or Discharge to Atmosphere element to represent the turbine nozzle.

`Note: the "Rating Curve" discharge element type is used when the discharge out of your orifice does not follow a typical orifice-equation relationship. It allows you to explicitly define the flow released out of the system for certain pressures at the discharge location. `

# Attributes

The following attributes are available when the "Discharge Element Type" is set to "Valve":

"Valve Initial Status" - This specifies whether the valve is initially open or initially closed.

"Time to Start Operating" - The valve starts to operate after this time, either opening or closing based on the initial status selection. It is measured from the start of the simulation. So a value of 5 seconds means that the valve remains in a fixed position for the first 5 seconds, and then starts to operate.

"Time to Fully Open or Close" - This is the time it takes for the valve to either fully open (if the initial status is closed) or fully close (if the initial status is open). It is measured from the "Time to Start Operating" value. Meaning, if the "Time to Start Operating" is set to 5 seconds  and the "Time to Fully Open or Close" is set to 10 seconds, then the valve closes linearly between time t=5 and t=15, and the valve is fully closed 10 seconds after it starts operating.

"Flow (Typical)" - This is the typical discharge out of the valve when it is open.

"Pressure Drop (Typical)" - This is the pressure corresponding to the typical flow through the valve. It is referred to as the "drop" because the pressure beyond the orifice is zero. The pressure and flow computed in the initial conditions will not necessarily be equal to these values, so you only need to enter any known pair. For example, if modeling a hydrant closure, you might enter the typical pressure and flow as the flow and pressure observed in a field test when the hydrant was opened.

You are basically defining an orifice size by way of the "typical" flow and pressure drop fields. By supplying one pair of pressure and flow, HAMMER can figure out the relationship based on the orifice equation that gives the pressure drop for any flow value. So, if unsure, you can use the orifice equation along with the size of your opening and an estimate of the "head" (pressure head drop) to solve for the typical flow. Selecting a pressure head drop close to a typical value you might see under normal operating conditions will yield the most accurate pressure/flow relationship during both the initial conditions and transient simulation. See further above under "How it works" for more information.

`Note: a standard 2.5 in. (100 mm) hydrant outlet would have a pressure drop of roughly 10 psi at 500 gpm.  `

When the Discharge Element Type is set to "Orifice," only the typical pressure drop and typical flow are available. When set to Rating Curve, only a rating curve table is available, where you would enter the table of head versus flow for your discharge. Initial conditions and transient head/flow is computed based on the values in this rating table.

# Example Model

The below model is an example of the use of the D2A element in HAMMER and has several scenarios for different configurations. Note:

• This example is included in recent versions of HAMMER, in the "Samples" folder within the installation folder
• The link below is to a version that can be opened in HAMMER V8i build 08.11.00.30 and above.
• Additional information can be found in the Project Properties
• You must be signed in to download the file. The link will not work if you are not signed in.
• This model is for illustrative purposes only

How do do WaterCAD/WaterGEMS treat the discharge to atmosphere element?

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