preface: I'm a mathematician by training, so I decided to treat this as a physics problem. This may or may not have any bearing on real life

I’ve heard it said that the water comes out of your shower at sufficient speeds that it can hit your watch and exceed the pressure rating, causing water to enter the case. Let’s examine the physics behind this. For measurement purposes, I’m measuring my Casio MTG1000. The buttons are about 3mmX7mm which is 21 square millimeters. Slightly less since it’s not a perfect rectangle, we’ll call it 20mm^2 for convenience.

This watch is nominally rated at 20 bar of pressure resistance. That is equivalent to 2 million Pascals, or 2 megapascals. For the sake of discussion, we’ll assume that the buttons are a weak spot and are only good for 10 bar, or 1 megapascal. We can ignore atmospheric pressure here because there is ostensibly air inside of the watch as well, negating that, so we only need to calculate instantaneous delta-P to figure out of that 10 bar button rating is met. 10bar is equal to 1 million pascals, which is in turn equal to one million newtons of force per square meter, which is in turn equal to one Newton of force per square millimeter.

A droplet of water is nominally 1 milliliter in free fall. 1ml of water has about 1 gram of weight under ideal conditions, sometimes a little less. If we assume that water leaves the shower head traveling at 10m/s (about 22 miles per hour, a very high estimate unless you are showering with a pressure washer). 1 gram x 10m/s ^2 = 0.01 newton.

Thus, the most force one drop of falling water can impart on the button is 0.01 newton per 20 mm^2 or 0.0005 pascals of force. In order to hit 10 bar, we would need: 10 bar = 1 million pascals = 0.0005 pascals per drop x some number of drops. Doing the math, it turns out that we would need around 2 BILLION drops of water hitting the same button at the same time. Clearly, this is impossible as the button is very small. Alternately, for one drop to generate 1 million pascals of pressure:

1 million pascals = (20 newtons)/20mm^2 and so for a 1gram drop of water to generate 20 newtons of force: 20 newtons = 1 gram x velocity^2 so velocity must be 141.421 meters per second, which is about 316.35 miles per hour (which some pressure washers can indeed manage).

Conclusion: showering with a watch, even if it is only rated to 3bar, should be perfectly safe unless you are using a pressure washer. Even if your buttons are smaller, (let’s say a hundred times smaller), you are still orders of magnitude away from being able to breach it with a shower, unless the manufacturer lied about the pressure resistance.

Thoughts?