Check the heating elements, one could be bad.

Yep. Probably lower heating element is in a couple inches of lime and has burned out.

An update: I tested both elements and they both read at 12.6 ohms, so I think they're okay. I also flushed the water heater and there wasn't much sediment. I got a thermometer and did a test of the water temperature drop at the laundry sink. It's actually not dripping particularly fast, but what's interesting is that the water is only 115 degrees when I have only the hot faucet on. Both thermostats are set at 135 and the sink us right next to the water heater -- just a few feet of piping away. Any ideas? Maybe a thermostat problem? Any ways to test the thermostats? Is it more likely to be the upper or lower?

Thanks so much for all your help -- am still learning how hot water heaters work. Thanks!

There's only one thermostat. It's used to control both elements.
Try taking the temperature from a bucket of water taken from the drain valve.

randy427, it's common on an electric heater for there to be two thermostats.

bostonbean2: The way it works is that the upper thermostat / element will operate first, heating the water at the top of the tank. When it's hot enough to switch off it then sends power to the bottom thermostat.

This way it provides a small amount of hot water quickly, then heats the rest of the water on the bottom of the tank.

You want to be sure that there's not a mixing valve anywhere that's causing the water temps to be low. Sometimes water flows backwards through a mixing valve and causes that problem.

Usually when an electric water heater puts out a small quantity of hot water it's because the lower element isn't heating. You can check this if you have an ammeter by testing the current through the upper element as a cold tank heats up first, then when the top shuts off, check the bottom element current.

You should be able to get the most accurate water temp reading by using a digital thermometer and taking the temp of water in a container at the TP valve. You should be able to flip the lever of the TP valve to hold it open long enough to get a good water temp reading. This will avoid any problem such as a mixing valve that might be throwing readings off.

I did some more testing. First, I tried checking the temperature of water straight from the TP valve -- it's also 115. I used my multimeter to test the thermostats using some instructions I found online, and it does seem that both the top and bottom elements are getting turned on at various times (top with the top thermostat turned all the way up, and bottom with the top thermostat turned all the way down and the bottom thermostat turned all the way up).

So I decided to set both thermostats to 150 to see what happened -- after leaving it overnight, the water in the tank is still 115 degrees. So now I'm stumped. Maybe still a bad thermostat?

BostonBean,

yeah, you got an odd one.

The thing is that I'm guessing you didn't check it with an ammeter. I'm guessing you checked with a volt meter to see if you had voltage, not confirm that that the elements were actually pulling the correct amount of current.

I have seen elements break and short to the lime on the bottom of the tank, for example.

So, without an ammeter test, you could just replace the controls and see if that works... and then replace the elements if it doesn't.

The definitive test would be with an ammeter though. If the current is correct, then it's the controls.