Make a Diving Depth Gauge

Frustrated by lack of cheap analog depth gauges around, I've decided to make my own. It turned out that it was very easy  to do so and gives appreciable result. So here's how to make a capillary type gauge that's relatively accurate up to 30 meters (100 feet) for about $1.

Sorry for the poor image quality. I may replace them someday, but I think these are good enough to illustrate the process.

To make the gauge, the first thing you will need is an ink tube from a ball-point pen. You could use any other piece of thin clear tubing, but I used a ball point pen tube. You need one that's straight, clear and as long as possible. It's diameter should be around 2 -3 millimeters (a tenth of an inch), bigger diameters will not work.  The tube will be the core of the depth gauge.
The next thing you will need is a piece of a hard flat ruler to glue your scale and tube to it. You will also need some epoxy resin and/or a laminator to glue and waterproof the printed scale, but I recommend you use both. You'll probably need a syringe, a syringe needle and some lighter fluid to clean the tube from the ink.

Note: Skip over this part if you are not interested in theory of operation and just want to make the gauge.

The gauge consists of a clear plastic tube whose end has been closed and a scale. When you dive, the surrounding water pressure compresses the air inside the tube, lowering its volume and allowing water to fill the rest of the tube. By knowing how volume of air and volume of water inside the tube relate, we know the pressure of surrounding water which is directly proportional to the depth. Therefore we can make a scale showing the depth according to length of air column.

Boyle's law
states that volume and pressure are inversely proportional. That means that if you double one, the other will halve. So at pressure two times larger than atmospheric, the volume of air inside the tube will be half of the volume at surface. Since tube is cylindrical, volume is proportional to length so we don't need to know the volume to determine the pressure (if length halves, the volume will too).

So if we know that atmospheric pressure is approximately 1 bar, we also know that the length of air column at 2 bar will be a half of full length of the tube. At 3 bar, it will be a third, at 4 a fourth and so on. But how do we know what pressure corresponds to which depth? Well we know that 1 bar is 100000 Pa or 100000 N/m^2. A newton roughly corresponds to weight exerted by object that weighs 100g. The density of water is 1000 kg/m^3. Therefore, a cube of water with 1 meter long edges would weigh 1000 kilos.
What we want to know is how tall would a cuboid of water with one square meter face have to be to weigh 100000 newtons or 10000 kilos. You could imagine that cuboid as a stack of those meter-edge cubes that weigh 1000kg. You need to stack them ten to get a 10000 kilo cuboid. So for every ten meters you get an additional bar of pressure.

So to get the pressure observed at a depth you have to add the atmospheric pressure of 1bar and 0.1 bar per meter - p=1+d/10. To get the length of the air column in the tube at that depth, you just divide the length of the tube by the pressure.

For those of you who are wondering how air doesn't escape from the tube, it doesn't do so because of the surface tension of the water. However, if your tube is too wide, it will come out and the gauge will be impossible to use.

To prepare the capillary you obtained from the ball point pen you first need to get the ink out. I do so by  taking the point out and blowing in the other end of the tube. Blow the ink out in a paper cup or something you'll throw away afterwards. Be careful not to stain anything with the ink because it's sticky and incredibly hard to clean. After you've blown out most of the ink, chances are you aren't left with a clean tube. Here's how I managed to clean mine: take a syringe, take out the piston, close the tip with your finger and pour some lighter fluid in it. Then put the piston back in and turn it upside down. Get the air out of it and put the needle on. insert the needle into the tube on the clean end and rinse the inside drop by drop with lighter fluid. Repeat if necessary.

After you've cleaned your tube, rinse it with water and allow it to dry. When dry, find the slight widening on one end of the tube where it used to be attached to the tip of your pen and melt it with a lighter to close that end of the tube. Be sure that the seal is airtight by blowing in the open end while the closed end is immersed in water and observing if there are any bubbles coming out. Measure your tube now (from the opening to the end of hollow part) as precise as you can, and you are ready for the next step.

Cut a piece of a plastic ruler slightly larger than the scale you've printed. Sand down the marks. Using epoxy resin or something similar, glue the scale to the ruler. I apply a layer of resin above the scale too, which is mandatory if you didn't laminate your scale. After the resin has cured, attach the tube along the line. The open end should be aligned with the upper end of the line. I use a few drops of super glue to get the tube fixed, and then apply epoxy resin along the tube. Be careful not to allow any resin inside the tube.

Your depth gauge is now ready. Go somewhere in open water and try it out. As you dive the water will enter the tube, but only to a certain level. That level shows you the depth at which you currently are. If you surface and there's still water inside, just shake it out. It's normal for that to happen sometimes, but not if there's more than few millimeters of water inside. If you get lots of water entering the tube, then the tube is too thick.