Thursday, March 9, 2017

Math Distraction

Our water heater has started to drip from the pressure-release pipe whenever we run the hot water. The troubleshooting guide in the manual says that this can be caused by "stacking", a condition in which short uses of hot water, which lead to the infusion of cold, cause the area around the thermostat to cool while the rest of the tank is very hot. That does not seem to be the cause here, for this morning I avoided all use of hot water until my shower, and the pipe still dripped.

On Tuesday, when my wife noticed his she called the plumbers. She then called me to ask what the volume of the water heater is. I said that I thought it was 50 gallons. That is correct, but I had never looked at the information on the heater; rather, about fifty years ago I heard fifty gallons mentioned as the volume of a particular water heater, and have since supposed most domestic ones to be of that size.

In trying to come up with a better justification, I thought, Suppose that the tank is sixteen inches across and five feet high. Then roughly speaking
  • The cross-section is 20 cm x 20 cm x pi, or roughly 1260 square centimeters
  • Five feet is 1.5 meters, 150 cm, giving the volume around 190000 cubic centimeters, 190 liters, a bit under 50 gallons.
 So 50 gallons sounded about right. I find that the tank is nearer 1.4 meters high, but I had figured the diameter as the trickier factor anyway.

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