How long can your shower be?

It's been a while since I wrote a satirical post on the blog. Although I have spread the good cheer and wrote elsewhere. The following is from a AFNash.com forum discussion. I'm afraid after seeing who asked the question, I may have abused him one too many times, but doggone it, he makes it so easy.

nate- I'm really curious as to how long you guy's get with a hot shower. I know it has a 30 gal tank, but I'm sure the hot water heater couldn't keep up with it that fast. Reason is, when we get back from long back-country hikes, I need to know how to "divide" up the shower time, and I'm just really curious to see what others on here get. I didn't plan on taking a 20-30 minute shower, but perhaps 10 minutes of hot water?

(Understand this is a 22 foot trailer with a 6 gallon water heater fired by propane, there were several comments about "Navy" showers before mine)

My answer:
Great question, lots of variables to consider. facetiously speaking however,

The final answer is: 8 minutes

I'm "assuming" a great many things here...

You like hot showers..
The water tank is 6 gallons (higher is longer)
The heating of the replaced water in the tank is exactly the same as the colder water introduced into the tank during the shower. (So we have exactly 6 gallons of hot water in the formula)

The temperature of the water in the tank is 180F (it may or may not be)(lower is shorter)
The temperature of the ground water is 50F (very common)(higher-longer/lower shorter)
(The temperature will vary depending on temp of the water in the hose, for a small amount of time)

If we use the formula (Va * Ta) + (Vb * Tb) / Va + Vb = T
Va = Volume of water in hot water tank
Ta = Temperature of water in tank
Vb = Volume of water from ground source
Tb = Temperature of ground water
T = total temperature of the combined volume
(6 *180) + (6 * 50) / 12 = T
1080 + 300 /12 = 115 degrees F.
Again an assumption made of half and half (6 gal. hot water and 6 gal. ground water)
Therefore we have 12 gallons of 115F water
Typical shower head flow restriction is 1.5 gpm
12 gallons / 1.5 gpm = 8 minutes.


Fire retardant suit on..

(It's not like I didn't leave hints in my comment "facetious", "assume", "fire retardant suit")

I only had one comment on it, RF said, Love it! Thanks...Wouldn't think of any kind of flaming response....

Props to you RF...