Pressure on heated water tank (rocket)

[solarblast]

Mythbusters did a test to see if a water heater would shoot through the roof of a two story building (home). They close all orfices, heated the water and it soared through the roof. They computed the final pressure as 85,000 pounds. As I recall they computed this by multiplying the area of the cylinder times its length times psi, then by another number, which they did not explain. 244. Maybe it was temperature (F). What law was used?

 

[russ_watters]

That's force they computed, not pressure. 244 is probably pressure in psi.

 

[solarblast]

Quite possibly. I can't go back to validate it though, since it has now been swept off my DirecTV.

 

[haruspex]

I cheated and watched it on youtube:
There is no magic extra term (and the length isn't in there either).
It's just pressure x base area = force.

 

[K^2]

As a general rule, physics in MythBusters is pretty terrible. The force on bottom of the tank is computed correctly, of course, but it's not a terribly useful quantity.

If you take a look at an earlier episode where they originally tested the water heater rocket, you can do some extra math. If you happen to have Netflix, it's episode 7 in Big Blasts collection. The episode is actually titled "Exploding Water heater".

In that episode, they launch a 30 gallon heater without the roof over it. They fill it to 80%, which seems to be a guess, but actually really close to optimal, and heat it up. It fails at 350PSI. Assuming adiabatic expansion of the water vapor from 20% to 100% of container, the amount of work done on liquid water is 69kJ.

We take these 69kJ, convert it to kinetic energy of water, use conservation of momentum (the tank is about 50kg) and we get initial velocity of about 71m/s. (158mph, 233 feet per second).

One more piece of the puzzle is terminal velocity for the tank. I estimated it to be about 75m/s. So the initial velocity is very close to it, and drag needs to be accounted for.

Taking drag into account, we get 5.8 seconds for tank to reach apex at 183 meters (600 feet), and 5.8 more seconds to plummet back down, for a total flight time of 11.6 seconds.

There is a shot in that episode that runs uninterrupted from boom to slam. Time it. It's pretty darn close to 11.6 seconds above.

What do MBs report the height as? 500 feet. Why? Because they simply took the 11-something seconds of air time, and assumed flight in vacuum. At 11.6 seconds, you get 540 feet this way. At 11.2 seconds, it's almost exactly 500 feet.

Moral? Don't trust their numbers. They don't know when an approximation is valid and when it is not.