This isn't really a K-fail, more of a K-mystery.

For months, I was dealing with a strange phenomenon. When I turned on my shower, I would have medium-hot water for approximately two minutes, at which point it would turn cold. You can imagine how unpleasant this was in an unheated bathroom in the dead of winter. My hygiene may have suffered slightly. I found myself showering at the gym a lot-- choosing the stares of old Korean women over the inhumane conditions of my own shower.

It wasn't until about 3 weeks ago that a friend of mine let me in on what is apparently an open secret in Korea: When showering, don't turn the water pressure on all the way. Only turn it about 80% on. I tried it, and was treated to a scalding (seriously: face-meltingly hot) shower that lasted (seemingly) forever. I was appalled. I still am. There is no logical reason for this to be happening.

First of all, my apartment is heated by hot water. It's pumped through the pipes under my floor that make up the ondol system I have gushed (pun intended) about frequently. My floor heats up approximately to the temperature of the heated seat in a car. This is no lukewarm rubber water bottle. That water is hot.

It stands to reason, therefore, that there would be enough of the stuff to give me more than 2 minutes of a  moderately hot shower at full pressure.

But say there isn't. Let's say that there is a limited quantity of hot water, and the pressure at which I run my shower determines how long I can take a hot shower. The math still doesn't add up. By reducing my water pressure by about 20%, I figure I should be able to extend my shower by about the same amount. Along those lines, the more I reduce my pressure, the longer my shower should be. But so far, I haven't found a significant difference between, say 50% water pressure and 80% water pressure. They both result in a very hot shower lasting around 40 minutes. Yet, if I turn the water up to full pressure, it turns cold in mere moments.

Let's keep my carbon footprint out of this for now. It's been really cold here, ok? Like... really, really cold. Also remember that I was taking 2-minute showers for months.

This is so baffling to me that I even tried to figure out a mathematical formula to illustrate the relationship between water pressure and length of hot shower. Seeing as I haven't taken math since junior year of high school, I obviously failed miserably.
 

Follow up at:  
K-Mystery Solved! (Caution: Science Ahead)