Readings: Bernoulli, Repo Markets, Hunger, etc.

Among the more useful things I know about complex systems, is this: When you fix a complex system under pressure, it either blows up again right away, or it doesn’t for a while.

I learned this when working in golf course maintenance, but was reminded of it again today when looking at what’s been going on in repo markets. Turning first to the golf course, the plastic irrigation pipes there would regularly break, sometimes shooting geysers impressively high in the air. When pipes broke you had to quickly turn the water off, dig out enough pipe to do a repair, and then wait a little for the glue to set. And a lot of leaning idly on shovels was involved, which was teenage-me-pleasing.

And then, the fun started: We would turn the watering system back on, and do a quick circuit of the golf course, looking for new breaks. While breaks could happen anywhere in the system, the most impressie ones were always in the same area: the 10th/18th fairway, which were side by side.

Why there? A little Bernoulli will help here. The total energy in a pipe with flowing, incompressible fluid can be approximated as follows:

TE = z + v2 / 2g + p/ρg

TE: Total Energy
z: elevation
v: velocity
P: pressure
g: gravitational constant

In short, the energy in a pipe is a function of the pressure and the velocity of the fluid flowing through it. If a larger diameter pipe flows into a smaller diameter one, the flow speeds up, but the pressure drops. You see that happen when you put your thumb on the end of a garden hose: You can now sneakily shoot water over your car and wet your kids, but the hose doesn’t blow up. You’re increasing the velocity, but keeping the total energy the same.

(This is Bernoulli’s principle, named after David Bernoulli, one of a family of maddeningly brilliant but pleasingly self-destructive Bernoullis, who discovered the inverse relationship between fluid pressure and velocity. And yes, it bothers me too that pressure doesn’t rise with velocity when you reduce the diameter of a pipe. I know it doesn’t, and I have always known it doesn’t, but it has never felt right, if you know what I mean. It feels almost sneaky — all that pressure just sitting there in big pipes — and I blame David Bernoulli. Maybe even his whole damn family of polymaths.)

Anyway, a picture might help here. In the following screen grab from a simulation I’ve been messing with where you can see how a changing pipe diameter leads, all else equal, to lower pressure, but higher velocity. Of course, this neglects friction, which causes velocity to be lower than it would otherwise be, thus raising pressure in the smaller diameter pipe somewhat, but let’s not get into that.

This is all well and good, you’re thinking, but what does it have to do with golf courses, let alone, you know, repo? Well, the trouble with this irrigation system was that it pumped water from a lake west of the course, up to the 10th/18 fairway, and from there up to the rest of the golf course.

This is a problem. Because the key word in the preceding sentence is “up”, and it occurs twice. There was about a 15m height difference between the pond and the two valley fairways, and another 15m height difference to get up to the holes above the valley. That’s a 30m difference, which turns out to be hugely important when it comes to pumping water. Why? Because water is heavy and doesn’t want to go anywhere, especially if water is sitting on water in a big column, like in a sloping pipe. Dealing with friction losses requires higher pump pressure, but dealing with sizable elevation differences requires much more effort, increasing the pressure in the valley pipes much more than would the case if, say, the pond was up on the ridgeline and the golf course was down below. (To be fair, this would introduce other problems, but no-one said golf course irrigation system design was easy.)

The upshot is that the reason why the most catastrophic blowups happened where they did was because the design was poor, causing the system to be hit with high pressure in a way that wasn’t obvious to onlookers. It also introdued unexpected sensitivies, like making it twitch about where sprinklers were turned on: if you didn’t bleed off some pressure  in the valley, the lower pipes were likely to burst; put too many sprinklers in the valley, and the ridges suffered.

Most compex systems are like this, of course. They are peacemeal, with pressure points in unexpected places that could be reduced or even eliminated by better design. In the case of repo markets, when everyone rushes into markets not designed for that sort of rush, weird things happen, like last night, when normally stable rates spiked in a way that, in essence, should never happen. (I analogized it to waking up in Los Angeles and briefly seeing New York in Pasadena, before it went back to New York again when everyone shouted at it.)

Maybe it was a technical issue, maybe it was a sudden surge of large financial services companies wanting to put assets in fear of a new Middle East conflict. Whatever. The effect was a massive pressure spike in repo markets, as you see below.

Like I learned a long time ago on golf courses, the main thing worth knowing about complex systems under pressure that they were never built for, is they either break away, or they break later. But later is never never.

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Here are a few articles and papers worth reading: