Last night I saw the newest episode of MythBusters. One of the myths they revisited was the exploding water heater. Well, it turns out that I had an analysis of this first explosion, but I didn't move it over when I switched software. So, here it is.
In case you never saw the first episode of exploding water heaters, here is the important part:
If you are impatient, here are the answers (from the video analysis):
- Time of flight = 11.8 seconds
- Max height = 167 meters = 548 feet
- Launch speed = 234 mph
- Speed on impact with the ground = 76 mph
First, from re-watching the video, I can see (and hear) that they used a 30 gallon water tank. By the looks of it, this tank is about 3 feet tall with a diameter between 1.5 and 2 feet. Can I find the specifications of this water heater (or one similar)?
No luck at Lowes, they had some 30 gallon tanks, but they looked too skinny.
Here is a shot of the one the MythBusters used:
How about Home Depot? - no. I found one that is an electric 30 gallon water heater. It is 36.5 inches tall and a 20.5 inch diameter. This looks good. I need the mass though. Well, I found a 40 gallon water heater that had a weight (with box and everything) of 115 lbs. I am going to randomly pick a weight of 75 lbs. (I am assuming that the water all explodes out at the beginning so that it is a projectile, not a rocket).
Here is the goal - to estimate how high this heater went? In the episode, they exploded a water heater without a house around it. This heater was in the air for about 11 seconds. I assume they used the same model in the water heater that went in the building. I would love to use the video from the first, building-less explosion but they did not have the camera zoomed out far enough. They probably did not think it would go too high. I need the dimensions to get a good estimate for the air resistance.
The questionable value is the coefficient of air resistance. The water heater should have a value between 0.4 (rough sphere) to 2.1 (smooth brick). I will try with each one and see what kind of results I get.
Actually, I need to go back and look at my first calculations. If you don't recall, I scaled the video by assuming the manlift was 24 feet. I would like to revise my scale. I found a manlift that comes with a 40 ft boom, that is what I will use. In the video, I measured the lift to be 41.8 mb (mythbuster units). This would make 1 mb = 0.29 meters. So, the initial velocity will be 365 mb/sec = 106 m/s.
So, here are the parameters I am starting with:
- mass = 25 kg
- radius = 0.26 m
- coefficient of air resistance = 1.4
- initial velocity = 125 m/s
This gives data similar to the data from the video (during the first second). Here is the data from the video:
And here is data from the numerical calculations:
One thing to note: First, this is not constant acceleration motion (although I fit a quadratic equation to the data). Nonetheless, a quadratic fit gives similar accelerations in each case (it is near to constant acceleration for the first second because the speed does not dramatically change).
Now to run the simulation for the full time and see how high it goes and how long it was in the air. Here is the answer:
- Time of flight = 11.8 seconds.
- Max height = 167 meters = 548 feet
- Speed on impact (ground) = 34 m/s = 76 mph (compared to 234 mph initially).
Assuming the initial speed were correct and there was NOT any air resistance, the height would be:
- time of flight = 25 seconds
- max height = 797 meters = 2,600 feet
This analysis seems reasonable. I do not have a speed for the heater on the way down because the camera was moving, but it clearly was moving slower than when it took off.
The above is basically what I posted after the original MythBusters episode on the water heater. I have noticed how much I have changed since then - look at the excel graph! What was I thinking?