The EPANET Manual suggests that the Gradient Method is used to solve a system of partially linear (conservation of mass) and partially non-linear (conservation of energy) equations in the form of AH = F. Since the method relies on the Newton-Raphson method to iterate to a solution, derivatives of the conservation of mass and energy must be taken.
In this video we show how to solve a looped pressure pipe system.
Some of the key concepts are:
First calculate the ‘resistance factor’ for each pipe in the system
Guess a direction of flow for each pipe
Pick a direction (clockwise or counter-clockwise) around each loop to sum the headloss
Write the headloss equation for each pipe
Write the continuity equation for each node
Guess the flow in each pipe
Compute the headloss for each pipe
Check the errors
Adjust the flow guess
Repeat the last two steps until the errors are below your chosen threshold
This type of network solution can be easily done for a very small and simple system. However, once you get more than a few loops, the solution becomes unmanageable and we need a better way which is typically a matrix solution like the one EPANET uses.
In the next post and video we will show exactly how EPANET uses matrices to solve network hydraulics.
In this video I briefly look at potential and kinetic energy using a ‘high school physics’ type of example of a ball on a hill. Then I relate that to hydraulics and present the Bernoulli energy equation and also introduce the Hazen-Williams empirical equation for estimating energy loss in a closed conduit. The concept of head is explained and Energy Grade Line (HGL) and piezometric head or Hydraulic Grade Line (HGL) are also included.
Steps to running a water quality analysis in EPANET:
Set Quality Options in the Data Browser to Chemical, Trace or Age. To analyze chemical breakdown such as chlorine, type the chemical directly into the box and it will be saved.
If you are analyzing a chemical such as chlorine, you need to enter the decay coefficients into the Reactions Options. You will also need to set some Initial Quality values at key locations in your network such as at a reservoir representing a water treatment plant clearwell. The initial quality will be the constant level of concentration that the constituent leaves the clearwell.
The length of the simulation must be long enough for periodic results to appear.
For water quality models to give good results, they often require a higher level of calibration than a planning level model.
Steps to set up an Extended Period Analysis in EPANET:
Set the Total Duration to be longer than zero hours. You can find the time settings in the Data Browser under Options. You also need to make sure the Pattern time step matches the pattern you will use.
Create a pattern of demand multipliers that will be used to factor the Demand up and down throughout the duration of the simulation. The video shows how to do this, but the basics are that you choose Patterns from the Data Browser and then click on the Add button to make a new Pattern. Type in the multipliers for each time step.
Now edit each Junction data to specify the Pattern you have created. This will cause EPANET to factor up and down the demand throughout each day.
Avoid using a Pattern ID of “1” since it can have unintended consequences.
Make sure the multipliers in the Pattern average to 1.0 for most cases.
This post and video correspond to the EPANET Users Manual section 2.7
To run a simulation, click on the run button (lightning bolt). If there are no errors, you will see a message appear that the run was successful. After that you can view output. You can view output in the following ways:
Show output on the map by clicking on the Map tab in the Browser. Change the selection under Nodes and/or Links to color the map based on output.
Toggle Node and Link legends by changing the setting in View menu -> Legends
Show output in a grid by clicking on the Table button. Select Links or Nodes. Add input data by selecting the Columns tab and check input data you want to display next to output data. Limit the number of rows in the grid by setting up a query on the Filters tab.
To toggle labels on and off, change the setting in View menu -> Options -> Labels
Double-click on a node or a link to launch the property editor. You can change any attribute, including the element ID. If you change a node ID, any link that is connected to the node will auto-update its connected node IDs
Reservoir head is a boundary condition that remains constant unless a pattern is applied.
Tank initial, minimum and maximum levels are measured as a distance above the Tank base elevation e.g. Tank floor
Hydropnuematic tanks can be modeled as very tall tanks with a small diameter. We will cover them in an advanced video.
Elevated storage tanks have some interesting issues. We will cover them in an advanced video.
Pump curves with a single head vs. flow point use a default equation to interpolate head at different flow rates. Pump curves with multiple head vs. flow points will do straight line interpolation between points