# Problem

Why does the system head curve generated by the program looks differently from hand calculations? Why does the curve not look parabolic sometimes?

Problem ID#: 3528

# Solution

It is important to understand that there are subtle differences between how WaterGEMS, WaterCAD, and SewerCAD computes system head curves versus how an engineer would compute a them by hand.

When one manually compute a system curve for a transmission line, (s)he generally ends up with a parabolic system curve (assuming you are using the Darcy-Weisbach formula where headloss is proportional to v^2). The process is pretty straight forward provided you have a single pipe, only one pump station, and no intermediate demands. But if you add some of those complications the calculations get much more difficult.

With WaterGEMS and WaterCAD, you can easily examine more complex systems - systems which would be practically impossible to solve by hand (e.g. multiple pumps, loops, demands, tanks, etc). WaterCAD/GEMS does this by computing the hydraulics for the network once for each point on your system head curve, as if it were a regular WaterCAD simulation. For example, say that you want a system head curve containing 5 points from 100 to 500 L/s (plus a point at 0 L/s), as shown below. WaterCAD would compute the model 6 times; once where there was no flow at the pump location, once when there was 100 L/s at the pump location, once where there was 200 L/s at the pump location and so on.

0.00 29.7
100.00 30.5
200.00 32.6
300.00 36.3
400.00 41.5
500.00 48.1

Note that this is "at the pump location" because for these calculations WaterGEMS/WaterCAD isn't using any pump information that you may have entered to generate the system head curve. Instead, behind the scenes, the program is merely applying a demand immediately upstream of the pump location and an inflow immediately downstream of the pump location, and then computing the resulting head difference. In other words, the pump is temporarily replaced in the calculation by two 'virtual' (i.e., not really there in your model) nodes. For more information on this process, please see chapter 8.6 ("Generating a System Head Curve") of the Advanced Water Distribution Modeling and Management book.

Furthermore, in a "closed system" where the system demands are supplied and no storage tanks exist, a system head curve is invalid, because there can only be one value of flow that the pump can pass - the value equal to the sum of all demands. In this case, the system head curve will not be valid except for that singular flow point and it's corresponding head.

The most common reason for the pump curve not to be parabolic is water consumption between the pump and the downstream tank. When this consumption occurs, it lowers the system head at low flow. In fact, if the consumption between the pump and tank is greater than the pump output(such that flow goes from the tank toward the pump), then there is an inflection point in the pump curve. If you want to check this out manually, put a single large demand between the pump and tank. WaterGEMS and WaterCAD, of course, handles this automatically.