(Inside Science) -- In developing countries, there is not always enough clean water for everybody who wants it, so supplies are scheduled to go to different neighborhoods at different hours of the day. When water flows to a new section, it can create spikes in pressure that break pipes -- leading to even less access to clean water. Solving these problems and making water more regularly available could be a boost for the residents in affected areas.
"I think this problem, in particular, is really ripe for optimization and doing mathematics on it," said John Wilkening, a mathematician at the University of California, Berkeley.
The problem can be significant. For example, two years of intermittent supply in Cyprus led to an increase of pipe ruptures by 30 to 70 percent each year, according to a 2012 study.
When a pipe bursts, precious water can leak to the ground, the ground can contaminate the supply, or the pipes can become blocked from collapse or dirt, making flows even less reliable than before.
Now, Wilkening and his team have begun developing a tool that could help water managers prevent pipe damage.
The team noticed that the existing models for water flowing through pipes, which are typically based on continuous flow, weren’t doing a good job of matching data collected in the field, Wilkening said. So the team decided to build a new model and create an optimization problem with it.
First came the model. The researchers modeled how water travels through the different pipes at different times, based on mathematical descriptions of water flow. They chose to consider a fluid with an average speed moving along one direction.
They tested on three existing datasets, and the model did a good job of matching up, he said.
Once they had a model, they created algorithms that can use it to spit out an optimal solution for minimizing pressure in the pipes while respecting a limit on the amount of water flow. It’s a challenging problem, Wilkening wrote in an email, in part because of the effect where a pipe in your house shakes violently when you turn on the water. So-called shock waves, which travel along pipes, are difficult for a computer to deal with.
The algorithms explored different combinations of when to turn control valves. Eventually, they came to a consensus on the best approach to minimize pressure.
The paper describing the results appeared in the SIAM Journal of Applied Mathematics on August 9.
Kara Nelson, a civil engineer at the University of California, Berkeley, who was not involved in the study but was on the lead author's Ph.D. dissertation committee, described the solutions as "elegant and also practical."
"I'm not sure that the work in this paper gets the modeling far enough along that it can contribute to designing intermittent water supply systems better," Nelson said. But she hopes it further engages the research community. She thinks there’s additional mathematical research and field data needed.
Srinivasa Lingireddy, an engineering consultant at Fluid Hammer, said similar optimization research has been going on for over 25 years. While the problem of intermittent flow is real and the idea of optimizing it could lead to improvements, he doesn't think the funds needed to implement a strategy will be available.
"Where do you get the investment for that?" he asked.
Zdenek Svitak, a civil engineer at the DHI Group in the Czech Republic who was not involved in the study but is developing processes for changing intermittent systems to 24-hour systems, said that any optimizations should take into account manual labor, since intermittent systems are often not automated.
"From [a] scientific point of view it is great and also there is great practical potential," he added.
Wilkening said the next step is to improve the modeling process, such as better capturing pipe junctions or studying contamination effects. He said the team's simulations could tell water managers when to turn on pipes.
"We are giving them guidance about what they can do with their current networks," he said.
He wrote in an email that managers could run the optimization just once and use the results to route water in the most effective way possible. He doesn't think the technology is very common in affected areas, but ideally there would be a centrally controlled automatic valve system. Or "at least people in the field with reliable watches," he wrote.
Optimization could lead to reduced water pressure, which may in turn lead to fewer pipe bursts. And consequently, maybe a little bit more reliable, clean water to go around.
Andrew Silver is a contributing writer for Inside Science. He has created interactive visualizations for Quanta Magazine and written for outlets such as Science, Physics World and Live Science. Follow him on Twitter @asilver360.