# Heat and cost estimates

A project log for Unity Candle

Taking the idea of a unity candle to the next level

I ran some estimates in a prior log about the heat output from this. The accuracy of this was restricted by some assumptions, namely that the pressure in the accumulator remains constant, and it assumed that only 1 valve was open. I had calculated this by using the flow rate of the valve from a datasheet. Instead, with some test data, we can recalculate based on the before and after pressure of the accumulator tank to determine the propane actually released.

The accumulator tank has a water capacity of 47lbs, which converts to 5.7Gal, and then to 0.76ft^3, I'll ignore the volume of gas held in the plumbing.
The average energy density of propane at room temp, atmospheric pressure is about 2450 BTU/ft^3.
Starting accumulator tank pressure is 60psi
Ending tank pressure estimated at 10psi

To calculate, we are going to figure out what volume the pressurized tank would need to be expanded to in order to get to atmospheric pressure. Rearranging Boyle's law, new volume = old pressure * old volume / new pressure = (60+14.7)*0.76 / 14.7 = 3.86ft^3

This is the atmospheric pressure volume of the entire accumulator worth at 60psi. Calculating again for the remaining gas after launching = (10+14.7)*0.76 / 14.7 = 1.28ft^3. This means that we released 3.86 - 1.28 = 2.58ft^3 at atmospheric pressure. With 2450 energy density, this means the output is 2450*2.58 = 6321BTU. This is actually remarkably similar to the original estimates. With 6321BTU of propane released in 1.5seconds, it could be compared to 15,000,000BTU/hr. If we take the burn time, (estimating 0.75sec burn time, it's probably a bit less), it would be 30,000,000BTU/hr when comparing to a furnace, so 300 times an average furnace in a 2500ft^3 home in the northern US. That is of course only sustained for that 0.75sec, as this system cannot maintain that rate due to evaporation rates of a 20lb tank, and the tank freezing.

For those curious, running the numbers suggests that a full 20lb tank of LP will last for about 55 of these blasts. Looked at another way, it is about US\$0.50 in propane per blast.

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