In which I am haunted by Bernoulli

I’m helping to get a new building finished and operational; this has been ongoing for some time. It’s for very sensitive equipment (atomic clocks of various flavors), so there are some stringent environmental controls, and it’s taken a little while to get the spaces to meet spec. The big problem has been the dynamic response — in steady-state, everything looks very good, easily meeting the 0.1 C tolerance, but it’s clear that the design didn’t quite anticipate transient responses. Because of the need for a robust system, there are a lot of redundancies, such as two take-off ducts for each room. All of the fine-tuning for heating and flow adjustments happen in the take-off duct, so there are two ducts per room, with one active and the other acting as a back-up. One room has been a particular thorn: it and its twin have the highest flow and largest heat load, and for some heretofore unknown reason, the two rooms would not behave in an identical fashion to identical changes. Whenever a duct change occurred, the one troublesome room’s temperature would fluctuate wildly, and there were smaller effects in other rooms.

Today the proverbial light bulb went on. The engineer who has been wrestling the building into shape discovered a design condition that probably falls under the category of the left hand not knowing what the right hand was doing. There is a static pressure sensor in the main supply duct, placed at some arbitrary point. There are also all of the take-off ducts going to the individual rooms, and the placement of the ducts and sensor was conflicting, and this is where Bernoulii steps in, moaning creepily, chains a-clanking and laughing (eerily, of course) because it turns out this has been a problem all along. You see, the pressure sensor was placed between two duct take-offs for the same room.

The Bernoulli equation is a statement of conservation of energy for fluid flow (technically for non-compressible fluids, and air isn’t, but the equation is a reasonable approximation at slower speeds). In the Bernoulli equation there are three ways you can put energy in a fluid: flow energy (i.e. kinetic, depends on speed), potential energy (gravitational) and pressure. Since this is a horizontal duct, there is no change in the potential energy, which leaves us with flow and pressure. If the flow energy (speed) goes up, the pressure must go down, and vice-versa with pressure changes causing flow changes. This is one way to explain why airfoils work (and I won’t get into the long-standing argument, but angle-of-attack is another way, which uses conservation of momentum. They both hold.)

Ok, so you have a pressure sensor before one duct (duct A), and it measures a certain pressure. Now, pretend a component in that duct fails, and you are forced to open duct B, while closing duct A. Well, the flow where the sensor is located drops — part of the flow is now going through duct B, and so the pressure goes up, as Bernoulli’s equation tells us. The building’s servo system thinks this is a problem and lowers the overall pressure, even though nothing had really happened to the airflow requirement in the building, and the ensuing responses were just wreaking havoc. Moving the sensor to the inlet end of the duct appears to be improving things.