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 m^{3}. The density of steel is about 8000 kg/m^{3}. 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 10^{7} 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.

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I suspect it's a 50 gallon water heater, possibly smaller. Using 18" diameter, 60" height and then subtracting 1.5" from the radius for pressure vessel, insulation, and case it would be 45.9 gallons and the insulation thickness may be greater.

Welcome, Rhett! Nice to have another physicist around; hope you like the new digs!

I agree with Rob. Here's a 40 gallon gas heater that's 18" diameter and 70" tall. If we assume that a gas heating element needs more space than an electric heating element, that would put the dimensions of the Mythbusters' tank at less than or equal to a 40 gallon heater.

Oh, and congratulations on your move to Sb.

The temperature is way too low. A water heater won't "explode" unless the water temperature is above the boiling point of water. A water heater might leak if pressurized with water below the boiling point but it won't "explode"

Water heater explosions are BLEVES, which stands for boiling liquid expanding vapor explosion. They occur when a liquid is superheated (that is heated above its saturation temperature) without boiling. The liquid then nucleates and boils explosively.

Usually this only happens when a vessel is filled with a liquid at its saturation temperature and pressure and then the vessel ruptures. The low pressure then propagates at the speed of sound through the liquid, now the liquid is at a temperature much higher than its boiling point, so it nucleates homogeneously and the nucleation propagates through the liquid as a true shock-wave, a discontinuous highly non-linear phenomenon.

This is also the mechanism for explosive volcanoes. A landslide depressurizes magma with dissolved water to below its saturation pressure, the magma then nucleates explosively. This is what happen in Mount St Helens.

A similar thing happens on a smaller scale when water is heated in a microwave. There are no nucleation sites or hot spots, so the water can heat above its boiling point and then nucleate explosively. Usually it is only a minor boiling, but if you put the water in a container that can withstand some pressure, then there will be a real explosion when the container ruptures. It can easily destroy the microwave and throw scalding water and steam everywhere, so donât do it.

Concur with everyone else. My 80-gallon heater at home is much larger than the one shown with Jamie.

Thanks for the feedback. I guess you guys are correct about the size (maybe I should have looked at my own water heater, but it is in the attic).

Also, @daedalus2u, if the temp is even higher then I am in even more of an energy deficit. But, you are probably correct.

I suspect the heater involved was a 40Gal tank due to size. I have installed several hot water heaters and this appears to be a 40Gal tank. Also I know this was an electric hot water heater because they had it hooked to an electrical generator. I did not see the wattage of the generator so cannot hazard a guess as to the electrical usage.

Isn't the boiling point elevated in a sealed water heater, same as in a pressure cooker? Isn't it possible that the vapor pressure increased to the exploding point before the water boiled? Perhaps the water boiled explosively after the bottom burst out, not before it burst? Because the bursting would lower the pressure and lower the boiling point at the same time, but the heat would all still be there.

The temperature of the steel and the temperature of the are not the same. I would guess you can safely ignore the rise in temp of the steel (its mass is also lower, so maybe this is a 10% approximation?) Also, I doubt going to a 40 gal. heater will help you at the last calculation: you're off by an order of magnitude, not by a factor of 2.

The problem is in your assumption of linearity. COLD residential water pressure is ~60psi, and the P vs. T curve is going be dead flat up to a substantial temperature. You can actually see this in the photo you have, the temperature trace is far from linear.

It is the empty water heater that is launched into the air, the water is left behind.

The water in a water heater is not uniform in temperature. Usually there are two heaters, and the top is significantly hotter than the bottom. The water inlet is at the bottom, and the outlet at the top. The hot water rises and there can be a significant inventory of hot water stratified above cold water.

The details of how the water is pressurized and heated and the details of the initial failure are quite important in understanding the dynamics. Without examining the aftermath, I speculate the mechanism is as follows.

Because the top is hotter, and metals have lower strength at higher temperatures, the initial failure is likely at the top, but no matter where the first failure occurs the course is pretty much the same. This depressurizes the water heater, homogeneous nucleation starts at the top and propagates down as a shock wave, hits the bottom and is reflected up. The pressure from the reflected shock is very high, that force cleanly breaks off the bottom of the water heater. The reflected shock now goes up and transfers momentum to the water heater which now has no bottom and launches it into the air.

The myth busters episode

http://mythbustersresults.com/myth-evolution

says it was a 52 gallon water heater. Choosing the cheapest ~50 gallon electric water heater from Sears, weight =130 pounds. The owners manual lists 2 heaters with wattage of 3800 plus 5500 watts for a total of 9300 watts. This water heater has a rated operating pressure of 150 psi. From the ASME boiler code, there is a factor of safety of ~3, so the boiler could be expected to fail at ~450 psi, but that is a saturation temperature of water of 456 F, which decreases the strength of steel. The fluid can either be saturated water (water plus steam at equilibrium), or subcooled liquid (water at a pressure higher than its saturation pressure (at its temperature).

At P= 315 psig (=330 psia) T= 426 F (at saturation)

50 gallons is 181 kg. 9300 watts * 41 min * 60 sec = 23000 kJ. The enthalpy change from 70 F to 426 F is 850 kJ/kg. 23000/850 = 27 kg. At most 27 kg of water could be heated up to 426 F. If we isoentropically expand the subcooled water at 426 F, 330 psia to 1 atmosphere (14.7 psia), then the enthalpy change is 71.5 kJ/kg * 27 kg = 1930 kJ of work. 130 lb = 59 kg. This gives a maximum possible velocity of 255 m/s.

When subcooled water at 426 F and 330 psia is expanded to 14.7 psia, the density goes from 841.6 kg/m3 to 3.00 kg/m3. This degree of expansion canât happen inside the water heater, however if the hot vapor contacts the cold liquid, the hot steam could condense. This could allow the expansion to occur to less than atmospheric pressure which greatly increases the energy available. If we let the expansion proceed until the temperature of the water is uniform, then the average enthalpy is 23000/181 kg = 127 kJ/kg = 124 F. Split the difference to maximize the delta T for heat transfer, T = 168 F. Enthalpy change is 151.6 kJ/kg = 4093 kJ of work = velocity of 372 m/s. This quantity of work is small compared to the total enthalpy of the system (23000kJ), so ignore that the temperatures would be slightly lower due to the heat converted into work.

There is plenty of energy and work available to launch the water heater at considerable velocity.

Welcome to Sb!

Very interesting start :)

I'm still confused. Is the tank completely full of water so that the tendency of the water to expand when heated causes the pressure to rise and the tank to burst? Or is the tank partly full of water so the increase in vapor pressure above the water bursts the tank?

In order to cause the burst, wasn't it necessary to close off the water inlet? If the inlet isn't closed, the pressure should be relieved by water flowing "upstream" out the inlet. Right? So this explosion would almost never happen in real life even if the thermostat failed and the pressure release valve failed. Or am I totally wrong?

@Robert,

I am pretty sure they closed off the tank completely (including the water inlet). I have no idea how much water they put in there, I would assume it is close to being full.

And yes, in real life, there are many things that would prevent this explosion from happening.

I've been doing research and may have some answers. I believe a full tank would burst at a much lower temperature, because the expansion of liquid water generates more pressure at lower temperature compared to the vapor pressure of a partly full closed system. The MythBusters needed the tank to burst at a high temperature to maximize explosive boiling so the tank must have been partly full. Also, the temperatures and pressures mentioned on the show are roughly consistent with data I found for vapor pressure.

I read that modern houses have check valves to prevent backflow into the water main, so it doesn't matter if the inclet to the water heater is open or closed. The open inlet used to be a safety factor in the old days when there were no check valves.

In real life, therefore, with a full tank of water in a closed system, I'm guessing the tank should burst at a relatively safe temperature even if the safety systems fail so you would get a flood of hot water but not an explosion.

Robert, many hot water systems have an expansion tank to allow for that expansion. There are relief devices for high pressure as well as for high temperature. The high pressure relief valves are sized to accommodate the full flow of steam from the heaters running at full capacity turning water into steam.

There is a very good history of the ASME boiler code out. It is worth a read. Before the ASME boiler code was implemented the death toll from boiler explosions was ~500 per year. A boiler and a steam engine was the only reliable source of mechanical work remote from a river and so was extremely valuable in manufacturing. People tolerated the death rate because that mechanical work was so valuable and there were no other alternatives.

It was finally a consortium of academics, boiler manufacturers, boiler users, and most important insurance companies that produced the ASME boiler code and which forced its use. If a building contained a non-ASME boiler, it could not be insured. If it could not be insured, it could not be used as collateral for a loan to expand the business. Many of the arguments against the ASME boiler code were like arguments against health care, it is socialist, it infringes on business owners' rights, it will hurt small businesses, the government shouldn't be involved (and wasn't mostly, building codes eventually did require it, but it was really insurance companies that mandated it first).