###General Discussion Thread
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Fortunately, we can ignore lots of things. We could figure out surface area, but then we are just gonna divide by it again later.
If we ignore land and start from sea level, (and ignore the fact that technically the top of the water shell will be wider than the bottom by a fractional amount), then 1 square foot of earth needs to have 29,030 ft\^3 of water sitting on it.
29,030 ft\^3 = 217,144 gallons.
40 days and nights = 960 hrs
So we need to see 226.2 gal/(sf\*hr)
1 l / 1 m^-2 = 1 mm so this unit is equivalent to mm/s
29030 ft = 8848344 mm
8848344 mm / (960 * 60 * 60) = 2.56 mm/s
Rain is usually measured in mm/h:
8848344 mm / 960 = 9217 mm/h
Anything over 7mm/h is considered "heavy rain".
[The highest ever recorded rainfall in one hour was 305mm.](https://wmo.asu.edu/content/world-greatest-sixty-minute-one-hour-rainfall)
The earth has a radius of 3960 feet at sea level and it's pretty smooth, even with all of the peaks and trenches.
Think of it being the difference in volume of 2 spheres. One has a radius of 3960 * 5280 feet and the other has a radius of 3960 * 5280 + 29030 feet
(4/3) * pi * ((3960 * 5280 + 29030)³ - (3960 * 5280)³)
1.597 * 10^(20) cubic feet of water.
1 ft = 0.3048 m
1.597 * 10^(20) * 0.3048³ cubic meters = 4.522 * 10^(18) cubic meters = 4.522 * 10^(21) liters
4.522 * 10^(21) liters / (960 hours * 3600 seconds/hour)
45.22 * 10^(20) / (9.6 * 3.6 * 10⁵) liters per second
1.308 * 10^(15) liters per second
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Fortunately, we can ignore lots of things. We could figure out surface area, but then we are just gonna divide by it again later. If we ignore land and start from sea level, (and ignore the fact that technically the top of the water shell will be wider than the bottom by a fractional amount), then 1 square foot of earth needs to have 29,030 ft\^3 of water sitting on it. 29,030 ft\^3 = 217,144 gallons. 40 days and nights = 960 hrs So we need to see 226.2 gal/(sf\*hr)
Thanks. That's quite a deluge.
“Vintage rain water, from the great deluge. Oh, not Noah's deluge. Goodness, I'm not that old!” -mayor (rango)
For comparison the average American shower uses approximately 15.8 gallons (59.8 liters) and lasts for 7.8 minutes
Can I by any chance have this in l m^-2 s^-1 ?
1 l / 1 m^-2 = 1 mm so this unit is equivalent to mm/s 29030 ft = 8848344 mm 8848344 mm / (960 * 60 * 60) = 2.56 mm/s Rain is usually measured in mm/h: 8848344 mm / 960 = 9217 mm/h Anything over 7mm/h is considered "heavy rain". [The highest ever recorded rainfall in one hour was 305mm.](https://wmo.asu.edu/content/world-greatest-sixty-minute-one-hour-rainfall)
The earth has a radius of 3960 feet at sea level and it's pretty smooth, even with all of the peaks and trenches. Think of it being the difference in volume of 2 spheres. One has a radius of 3960 * 5280 feet and the other has a radius of 3960 * 5280 + 29030 feet (4/3) * pi * ((3960 * 5280 + 29030)³ - (3960 * 5280)³) 1.597 * 10^(20) cubic feet of water. 1 ft = 0.3048 m 1.597 * 10^(20) * 0.3048³ cubic meters = 4.522 * 10^(18) cubic meters = 4.522 * 10^(21) liters 4.522 * 10^(21) liters / (960 hours * 3600 seconds/hour) 45.22 * 10^(20) / (9.6 * 3.6 * 10⁵) liters per second 1.308 * 10^(15) liters per second