System Head Curve

Hi Amine,

We get a lot of questions about system head curves in WaterCAD, and most of them come down to the subtle but important differences between how WaterCAD computes them versus how an engineer would compute a system curve by hand.

As you mention, when you manually compute a system curve for a transmission line, you generally end 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 calcs get much more difficult.

With WaterCAD you can easily tackle more complex systems - systems which would be practically impossible to solve by hand (e.g. multiple pumps, loops, demands, tanks, etc). WaterCAD 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 simulaiton.

So, say 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 200l/s at the pump location and so on.

Example System Head Curve: 

Flow               Head

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 I say 'at the pump location' because, for these calculations, WaterCAD isn't using any pump information that you may have entered. Instead, behind the scenes, WaterCAD is merely applying a demand  immediately upstream of the pump location and an inflow immediately downstream of the pump location, and then figuring out 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 which I will call a 'suction node' and a 'discharge node'. I have attempted to illustrate how this works in the attached figure (note though that you don't ever actually see these 'virtual' nodes in WaterCAD).

Now because WaterCAD is solving your entire network to work out the system head curve, there are many reasons why your resulting curve might not be parabolic. For example, there could be another pump station in your system which turns off at some point due to a pressure control; or a flow control valve might start to influence the system curve above a certain flow; or the supply of all the system demands might mean flow needs to travel a much longer distance into a storage tank, etc. (Actually, systems where the demands are supplied and where there are no storage tanks - sometimes called 'closed systems' - are a particularly special case, but that is probably a topic for another thread). Even the concept of 'static head' is difficult in a complex network because if you have, say, a second pump station in the network, your 'static' head at the first pump station will most likely depend on whether the second pump is on or off! But in the end, what WaterCAD gives you is a real system head curve because, according to your model, it is truly the head a pump would need to provide to deliver a certain flow.

Hopefully this has helped shed some light on the system curve calcs. One thing you may like to try is to try and manually recreate the results of the system curve calcs by replacing your pump with a 'suction node' and a 'discharge node' (as shown in the attached figure). This might help you understand the calculations for your particular system.

Regards,

Mal Sharkey

Product Manager
Bentley

Very good discussion, Mal.

 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 out put(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. WaterCAD/GEMS, of course, handles this automatically.

 If you want to learn more about pump curves, get a copy of the paper

 Ormsbee, L. and Walski, T. "Developing System Head Curves for Water Distribution Systems," Journal AWWA, Vol. 81, No. 7,
July 1989 .

You realistically won't get a sensible result if you run a WaterGems System Head Curve on with Flow Control Valves in-line, and representing the inlet valves to the tanks.   I would also recommend that you don't model each of the 13 tanks as separate model tanks, and rather combine these into 1 large model tank.........you also won't get sensible results if you have tanks that are hydraulically close.

From your descripton of the inlet valve, a TCV is perhaps more representative of what is there.  With the TCV you can either input k values directly, or define a Valve headloss coefficient vs Valve Opening Ratio curve.  To borrow one of Tom's phrases, "Model what you have".

Thanks for your reply Ben..

I will try the TCV and let you know outcomes. 

On the other issue, I cant model the 13 tanks as one since this will not give any appreciation to the difference in levels in the tanks and therefore I wont be able to produce an accurate system curve. Also I have to try different scenarios, running tanks 1 2 and 3, then 4 5 and 6, etc. And then generate required operation points for each scenario.

I agree with your recommendatio that running the model for multiple tanks is not recommended, proven by my trial to run the model to all tanks without the flow control valves on each tank inlet. The model is over sensitive with regards to levels, and sooo uncontrollable. But the flow control valve at each tank inlet smoothens the model and tunes the results very well, and they will be present in the final design not just in the model.

Yup, I've been in that situation before!  I hate to say it, but it doesn't lead to anything good :-(

As you've noted, with hydraulically close tanks you'll get severe fluctuations in tank flows/levels in the model..........just be aware that in reality theses are actually smooth, what you see in the model is just a limitation in the ability of the calculation engine to precisely calculate a tank's level.  Even a 0.1 mm error in tank level in the model calculation can yield extreme model flow rates between tanks.   In reality, the tanks will operate in equilibrium with each other.......so the model results are artificial in this respect.

With the tanks that sit next to each other, you will often find they have varying physical elevations and dimensions from each other.  The trick in the modelling world to get them to behave as "real" tanks will is to use 1 tank for all tanks that are close to each other and "balancing" each other......but with a Variable Area.   ie. Use a spreadsheet to calculation a combined Depth vs Volume curve for all of the tanks, and input this into the model.

I have also used the FCV "trick" in years gone by for smoothing flows into tanks.........but I've thrown the method out, as the negatives far outweighed the positives, as it didn't show a "real" result but rather something quite artificial.  It was primarily because I had been using hydraulically close tanks, and haven't needed to use dummy FCVs anymore once I started combining tanks together.

Out of curiousity, why are using FCVs in the Tank design?  (As opposed to say normally an Alititude Valve or Regulator Valve (ie. TCV))

Ben..

I dedicate the conceptual approval I obtained to you. Thanks alot for your help. Sorry it took me a while to answer but I was busy in the submission and presentation, and mainly incorporating ur advices.

I changed the close tanks to one body and realized that this might actually allieviate the need for FCV's at the tanks inlets. Previously I obtained an impossible fluctuating output which cannot be presented, meaning that I wrongfully added some of the FCV's to control the system while like u said the systems in operation are not that sensitive like the model.

The question which keeps invading me from everywhere and no literature was good enough to say is as follows, this is not the case I am solving, its just a question representing the many cases I am facing:

If you have a pumping station at invert level 0.00 meters, feeding a water tank with a bottom level of 100 meters, and a maximum level of 5 meters (total 105 meters), but we have a junction A (high point) at the middle of the pipeline (before the tank) with an elevation of 130 meters. Even if you design the pumping station to cater for the high point  A in the middle , the model ignores this high point A and conveys water from the pumping station to the tank only creating negative pressure at

 junction, which leaves the model with no value. My first question is this what actually happens on site, does the pump adjust itself for the tank only and ignores the high junctions in between? In true life is it not possible to enter the tank with pressure, the issue in which the model is rejecting and keeps altering the hydraulic gradeline to enter the tank with zero pressure. What is the solution for this in the model and in operation if occurs?

There are several cases which you need to consider in this design.

1. If the hydraulic grade line (HGL) is always greater than the elevation of the high point, then the pipe will remain full and behave as any other pressure pipe would. If you want to force this situation, use a smaller diameter pipe (or a pressure sutaining valve)on the downstream section of the force main to raise the HGL at the high point.

2. The HGL is below the high point elevation:

   a. If you have an air release valve at the high point, the pump will pump up to the high point, you will have a section of partly full flow and at some point flow will tranistion back to full pipe. Use the WaterGEMS/SewerCAD air valve to simulate this.

   b. If you do not have an air release valve at the high point, you may be able to siphon over the high point but you are asking for trouble. The pipe can get blocked with air or if the HGL drops too far, below the vapor pressure of water, the water can oscillate between vaporizing and condensing and you have all sorts of trouble. Avoid this case.

 This type of situation is more likely to exist in a sewer force main (rising main) than a water distribution pipe. More regulatory agencies will not allow you to have a section of a treated water main with atmospheric pressure. Since this condition is more of a sewer force main issue, it is described in Bentley's Wastewater Collection System Modeling and Design book.

If you regulations require that you maintain some minimum pressure in the distribution system, then you would install a pressuer sustaining valve somewhere in the downward sloping section. (If you include a PSV in your model, don't include a air valve.)

 Tom

There are several cases which you need to consider in this design.

1. If the hydraulic grade line (HGL) is always greater than the elevation of the high point, then the pipe will remain full and behave as any other pressure pipe would. If you want to force this situation, use a smaller diameter pipe (or a pressure sutaining valve)on the downstream section of the force main to raise the HGL at the high point.

2. The HGL is below the high point elevation:

   a. If you have an air release valve at the high point, the pump will pump up to the high point, you will have a section of partly full flow and at some point flow will tranistion back to full pipe. Use the WaterGEMS/SewerCAD air valve to simulate this.

   b. If you do not have an air release valve at the high point, you may be able to siphon over the high point but you are asking for trouble. The pipe can get blocked with air or if the HGL drops too far, below the vapor pressure of water, the water can oscillate between vaporizing and condensing and you have all sorts of trouble. Avoid this case.

 This type of situation is more likely to exist in a sewer force main (rising main) than a water distribution pipe. More regulatory agencies will not allow you to have a section of a treated water main with atmospheric pressure. Since this condition is more of a sewer force main issue, it is described in Bentley's Wastewater Collection System Modeling and Design book.

If you regulations require that you maintain some minimum pressure in the distribution system, then you would install a pressuer sustaining valve somewhere in the downward sloping section. (If you include a PSV in your model, don't include a air valve.)

 Tom

As a supplement to Dr. Walski's post: If you decide to use the air valve approach in WaterGEMS, WaterCAD or SewerCAD, you may find the following technotes useful:

For SewerCAD

For WaterCAD/GEMS

Jesse

Thanks doctor Tom,

 I tried the sustaining valve at the end and it is working properly. I will be trying the air valve at the coming stages i nthe analysis.  However, does this mean that I really need a sustaining valve to be installed in the system on field, or this is only to manipulate the model?

Refereing to the case I first asked about, if I estimate the head and flow required at the pump considering the minimum required pressure setting at the PSV to keep the entire network at positive pressure, I used this point (flow and heat) as teh operation point for purchasing the pumps, but on site I didnt install the sustaining valve , would the system operate within the point estimated in the presence of a sustaining valve, or it will be lost and choose to run at lower flows until the siphon works?

What is the real case?

Is the model with the way it is without any control valve or air valve,depicting the actual conditions, that the high point will be overcame through siphons eventhough we didnt consider it in the model, and it is given that the pressure is negative at the high points? will this estimated flow really pass if we apply the siphon?

You're asking the right questions.

In the field, you would install an air release valve. In the model you can treat it as a PSV with a 0 setting or AV. You will get the same results.

The PSV and AV will only keep the system pressurized up to the high point for the AV or the PSV locations wherever that is. Downstream of the valves, the system can transition to gravity flow depending on the head loss between the valve and the end. When you turn off all the pumps, the system will drain downstream of the valves. A mechanical PSV needs some flow through it in order to operate.

If you must keep the pipe full even when the pumps are off, then you need a control system that will close a valve at the pipe outlet just before the pump turns off and slowly open that valve as the first pumps turns on. It can be set to throttle to maintail a positive pressure throughout. The controls for this can get sophisticated.

There are some more exotic options. You can consider tunneling through the hill. That will greatly reduce energy usage.

If the flows are high enough, it may be possible to install a micro turbine at the outlet and recover the energy used to pump over the hill.