So, with all my concentration on high pressure air compression, specifically to get to 3,000 psi in the quickest way possible, I suppose it was only a matter of time before I casually wondered at what ocean depth 3,000 psi would be felt.
So on my way in to work this morning, while sitting at a traffic light, I tried to guesstimate the depth.
It’s pretty straightforward, but doing so while driving reduces your resources to pretty much just your own brain.
So I started with the basics. Water is fairly difficult to compress. For all practical purposes you can consider water to be incompressible, meaning that density of water at depth is the same as the density at sea level. Also, the pressure of water at depth, just like air pressure on the surface of the earth, is essentially just the weight of all the water or air stacked up to the surface of the water or edge of space. That means if you took a column of air one square inch but extending upwards 400 miles or so, you’d have 14.7 pounds of air.
So what I had to figure out is how high a column of water one square inch in cross-section would need to be to weigh 3,000 pounds. That simple.
So, how high does a 1 sq inch column have to be? Well, I knew that one cubic centimeter of water weighs one gram, but I don’t have any English weights and measures memorized, not reliably. I thought a gallon of water weighed about eight pounds, but I wasn’t sure of that. So I had to convert cubic centimeters into cubic inches, then convert kilograms into pounds…
I came up with a depth of around 6,200 feet. The actual value is about 6,700 feet. So my traffic light guesstimate was well within 10% of the actual value. Not too bad for a two minute in the head calculation. (Actual error was almost exactly 7.5% error…)