Importance of fire flows to calibrate water distribution models

Over the years, I have found several engineering projects and journal articles in the topic of modeling water distribution networks. One common mistake that I found in most of them is that they "calibrate" the model (pipe roughness) considering only normal flow conditions instead of high demand conditions such as fire flow tests. Actually, it is not possible to calibrate a model without considering high demand conditions. 

Water distribution modelling: The physics and mathematics

There are several water distribution models (water distribution software) such as EPANET, InfoWater, WaterGEMS, Mike Urban and others. It is important to remember that water distribution models are based on physical processes and they simulate the network by solving a matrix system based on:

• Conservation of mass in every node
• Conservation of energy in every pipe

In the conservation of mass we have 3 variables:

• Flow. This is a known value. Is a boundary condition.
• Area. This value is calculated based on pipe size (known value)
• Velocity. This is a function of flow (known value) and pipe size (known value)

In the conservation of energy we have 4 variables:

• Pressure. This is the value to be calculated
• Velocity. This is a function of flow (known value) and pipe size (known value)
• Elevation. This is a known value
• Head losses. This is a calculated based on the Hazen-WIlliams equation, which is a function of flow (known value), pipe size (known value) and pipe roughness (to be calibrated)

Thus, we have 2 unknown values: pressure and pipe roughness. By assuming a proper pipe roughness we can calculate the pressure. This process of assuming the proper roughness is the calibration of the model. 

Fire flow and pipe head loss

Head losses are calculated based on the Hazen Williams equation. Hazen Williams equation relates the friction head loss as power function of the flow. Thus, it becomes more sensitive to higher flows (you can solve the Hazen-Williams equation online). Let’s show one simple example.

Let’s assume a 1 km pipe reach of a 250 mm pipe, and considering different roughness values from 130 (new pipe) to 70 (pipe in a very bad condition). Let’s calculate the pressure drop for different flows between 1,500 cmd and 5,450 cmd. We are assuming typical flows (1,500 cdm and 5,450 cdm) because:

• Assuming a 300 l/hab day, 1,500 cmd would be enough to supply water to a 5,000 habitants zone
• 5,450 cmd is equivalent to a standard fire demand (1,000 gpm)

As we can see, considering a 1,500 cmd water flow would led to accept a wide range of roughness values. We could assume any roughness value between 70 to 130, and pressure differences would be 1.3 m (about 1.9 psi). On the other hand, those roughness values (between 70 to 130) with fire flow demand produces a 14.5 m pressure difference (about 20.5 psi). Thus, high flows such as fire flow really show the sensitivity of the pipe to roughness. 

Suggestions to calibrate water distribution models

Basic suggestions for calibrating water distribution models are:

• Use normal conditions data to verify connectivity issues only. Do not use it to verify roughness. 
• If you want to calibrate the model, then perform fire flow tests or collect data during high demand equivalent or greater than 1,000 gpm.
• If is not possible to collect high flow data, do not say that your model is calibrated (because it is not). In this case perform a sensitivity analysis.