Eureka in the Hot Tub

This sounds almost impossible to believe but I had an Archimedes-like "Eureka Moment" the other night. And it even had to do with the displacement of water in a bath. Let me explain. I have been struggling for months to figure out why the venturi jets in our Florida home's hot tub work intermittently. Oh, the jets draw water all right but they don't pull in the air stream that makes for those refreshing bubbles. I have been asking everybody who seems to know anything about it why it doesn't seem to work. Or to be more exact, works only at times.

One way we've gotten the jets to bubble is to pull out the filter cartridge which is in line with the pump feeding the hot tub. When the filter is out, the pressure drop in the line goes down and the velocity of the water moving through the pipe goes up. Somewhere in the deep recesses of my mind, I remember Bernoulli's Equation which states that the pressure varies inversely with the square of the fluid velocity. Speed up the fluid and the pressure drops enough to suck air into the jets. The trouble with this is rather obvious. Who wants to go out and pull out the filter every time you want to use the hot tub?

A really smart pool guy came by the other day and looked over the situation. He looked at the location of the venturi air tube that comes out of the tub and diagnosed it as having been installed too low, hence the amount of water that had to be pulled through the tube to bring in air was too high. But the tube is set in concrete, not easy to move.

So back to my Eureka Moment. My son and I got in the tub the other night to try to puzzle out the problem. I displaced my volume of water out the overflow trough into the pool. The water surface level didn't change. But when I got out to get a towel I took my volume out of the pool, the water level dropped, and, "Eureka!", the bubbles started. The lower water level was just enough to pull the air into the venturi air tube. We were ecstatic to see that the tub worked and, wonder of wonders, Bernoulli's Equation told us why. The pressure is not only inversely related to the velocity of the fluid, it is also inversely related to the height of the column of water in the air tube. Lower the hot tub surface and the height goes down increasing the vacuum pressure to suck open the air tube. We finally understood how the system worked and with that knowledge we can make it work consistently.

So what did I learn out of all this? Observe carefully and make notes on what you observe. Look for correlations between changing one variable and the response in another parameter. Try to understand the physics. Hypothesize about what is happening but always be open to the happy accident, the Eureka.

Archimedes would surely have been proud of us. And Bernoulli, too. Centuries have passed since these two intellectual giants showed the way. There is something very comforting in seeing that the laws of physics are as applicable today as they were then.

I gotta run. The hot tub is calling.