Energy in an exploding water heater

The more I think about the last MythBusters’ exploding water heater, the more cool things I see. How about I look at the energy of the explosion. There are three things I can look at:

• How much energy went into the water heater from the electric source?
• How much kinetic energy did the water heater have right after the explosion?
• How much thermal energy did the water and water heater have?
• How much gravitational potential energy did the heater have at it’s highest point?

Hopefully, I can show that the energy in from the electric source is greater or equal to kinetic plus thermal. Also, the gravitational potential at the highest point should be less than initial kinetic energy (because not all the water went up and some energy was lost due to air resistance). Let me take it one piece at a time.

Electric energy input

To look at the energy input, I can start with the power consumption of the heater. Then, if I know how long the heater was on I can use the relationship:

So, how long was this thing running? I think I have the answer. The MythBusters were kind enough to call out pressure and time data. Here it is:

The pressure seemed to increase at a fairly linear rate. Also, from this I can see that the time the heater was on was about 41 minutes. Next question: what kind of water heater was it and what kind of power does it use? Lowes lists the 80, 50 and 40 gallon as the popular sizes. From this picture, I am going to totally guess it is an 80 gallon type since it is 5 feet tall.

Almost all of them were listed as 4500 watts. There was one listed as 5500 watts, so I will go with the more popular one. Now, I have the time, I have the power, I can calculate the energy put into the water heater.

Where does all that energy go? Right after the explosion, it goes into:

• Kinetic energy of the water and heater
• increased thermal energy of the water and the metal in the heater
• increase in structural energy needed to break the water heater (I will assume this is small compared to the other two)

How much of it is kinetic energy? This depends on the mass and the velocity. Adam says that he calculates the velocity to be 350 mph (156 m/s). What about the mass? Let me assume it is an 80 gallon tank. So, I guess it has 80 gallons of water in it. The mass of this water would be 304 kg. What about the rest? I search for at least 10 minutes online and didn’t come up with the thickness of the walls nor the mass of a typical water heater. Let me ball park guess that it is 1/4 inch steel. This would be a volume of steel of:

Here, d is the diameter, l is the length (height), and s is the thickness. At one point, Adam states that the water heater is 18 inches in diameter (0.46 m) and it is about 60 inches tall (1.52 m). Using this with the 1/4 inch steel, I have a volume of steel = 0.016 m³. The density of steel is about 8000 kg/m³. This would make a mass of 128 kg (280 lbs). That seems too high.

Why didn’t I check Sears? Here is an 80 gallon electric that lists the weight:

I will go with a mass of 80 kg. This will give a total mass of (80 kg + 304 kg) 384 kg. Now for the kinetic energy:

The best thing about this answer is that it is less than the electric energy that went into the thing (it would be really bad if there was more kinetic energy output than electrical energy input).

Now what about the thermal energy? I need to first know the temperature. I don’t know this value of temperature when the thing exploded. I am going to have to use a couple of clues. My first clue is that the the pressure and temperature seem sort of linear – check out this screen shot:

I claim that the top graph is the pressure data and the bottom one the temp. Suppose that I assume the pressure increases linearly with time. Then, here is one data point for pressure and temperature (P = 61.4 psi and T = 108.7 F). For the second water heater explosion, they show another shot of the screen.

Here P = 177.5 psi (and red) and T = 148.3 F. Yes, this is a different water heater, but it is the best I have. Using these two data points (and assuming linear relationship) the temperature when the pressure is 315 psi would be 195 F. Assuming the water starts at 70 F, what would be the change in thermal energy?

Here, the C’s are the specific heat capacities of the materials. For water, this is about 4200 J/(kg*K) and for steel, this is about 450 J/(kg*K). Putting in the masses of the two things (water and heater), I get an increase in thermal energy of 9.1 x 10⁷ Joules. This is not good. This is more than the energy that went into the water heater. Hmmmm.. Where could I have gone wrong? I can think of a couple.

• Maybe their water heater was using more than 4500 Watts.
• Maybe their water heater wasn’t all the way full
• Maybe I grossly mis-estimated something somewhere.
• Maybe the final temperature was much lower than what I estimated (very likely)

I have nothing more to say.