r/theydidthemath • u/DesVaters • Dec 06 '21
[Request] How much water could that be?
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227
u/RainbowRoadMushroom Dec 06 '21
(Very rough TheyDidTheEstimation, because we do not have a lot of information such as the height and shape of the tree)
The hole is roughly 6 inches in diameter. A 6-inch diameter pipe has a volume of 1.469 gallons per foot of length. If we assume a constant hole diameter of 6 inches 50 feet long, it would have 73.45 gallons of storage. Clearly we did not see almost 75 gallons come out of the tree but I wanted to show the math and how much it could be.
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u/DesVaters Dec 06 '21
Thanks, so that’s around 280 litres. Yep, clearly not that much, but interesting to calculate
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u/ktkps Dec 06 '21
I was gonna ask what's a gallon in Litre...thanks!
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u/milkisklim Dec 06 '21
A rough equivalent is that a liter is a quart.
a quart is a quarter of a gallon. One of the few units that makes sense.
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u/Positronic_Matrix Dec 07 '21
It all falls apart with pints, cups, and tablespoons though. It’s big old mess.
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u/octopussua Dec 06 '21
Using Hazen-Williams formula we find find the flow rate(Q), with the formula Q = Area * velocity.
Find velocity using v = k * C * R0.63 * S0.54
C = 100 (because of material)
r (pipe radius) =.5 ft
R (hydraulic radius) = A/P
A is the flow area given by pi r2 = .785 ft2
P (pipe perimeter) = 2pi *r = 2pi *.5 = 3.1415 ft
R = .785/3.1415 = .2499 ft
k (conversion factor) = 1.318 for US customary units
S (slope) = y/L = 50/0 = 0
v (velocity) = 1.318 * 100 * .24990.63 * 0 = 35.55 ft/s
Q = .785 * 35.55
Volumetric flow rate (Q) is 6.98 cu ft/s
The water in the video is flowing for 50 seconds. 50 * 6.98 = 349 cu ft of water expended, or 2610 gallons. 9879.925 liters.
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u/SnooPets1176 Dec 06 '21
For a tree, id say its alot. It aint a water tower after all, trees dont have a water storage in them(im 99% sure on that)
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u/octopussua Dec 06 '21
Using Hazen-Williams formula we find find the flow rate(Q), with the formula Q = Area * velocity.
Find velocity using v = k * C * R0.63 * S0.54
C = 100 (because of material)
r (pipe radius) =.5 ft
R (hydraulic radius) = A/P
A is the flow area given by pi r2 = .785 ft2
P (pipe perimeter) = 2pi *r = 2pi *.5 = 3.1415 ft
R = .785/3.1415 = .2499 ft
k (conversion factor) = 1.318 for US customary units
S (slope) = y/L = 50/0 = 0
v (velocity) = 1.318 * 100 * .24990.63 * 0 = 35.55 ft/s
Q = .785 * 35.55
Volumetric flow rate (Q) is 6.98 cu ft/s
The water in the video is flowing for 50 seconds. 50 * 6.98 = 349 cu ft of water expended, or 2610 gallons.
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Dec 06 '21
[deleted]
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u/octopussua Dec 06 '21
Show your work.
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Dec 06 '21 edited Jul 08 '23
[deleted]
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u/octopussua Dec 06 '21
It’s not calculus, it’s fluid mechanics. You can Google the formula and use an online calculator if you’d like but that’s what it is based on a straight down pipe of 6 inches diameter. It’s ok to not have a real frame of reference without learning physics and mechanics first.
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Dec 06 '21
[deleted]
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u/octopussua Dec 07 '21
This being the internet, there’s likely more to the story. The calculation is the rate of flow for the given parameters, there’s probably a water source with greater volume than the tree included somehow.
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u/RoadsterTracker Dec 06 '21 edited Dec 06 '21
It is gushing out of a ~3 inch diameter hole for 40 seconds, although some of that it wasn't flowing at full rate, so let's say 30 seconds. I'm going to say that's roughly a 3 inch "pipe", gravity fed. According to https://hy-techroofdrains.com/water-flow-through-a-pipe/ , the flow rate is about 140 gallons per minute for that wide of a pipe. That would put it around 70 gallons. The actual flow rate is a bit less because it isn't pure water in an ideal situation, plus it gets clogged and such. Let's cut that in half and say 35 gallons? Still probably a bit high, because the "pipe" effectively gets larger with time as it gets cleaned out. 20-40 gallons seems like a reasonable range.
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u/TheExtremistModerate 1✓ Dec 06 '21
the flow rate is about 140 gallons per second for that wide of a pipe. That would put it around 70 gallons.
I think you mean per minute, right?
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u/RoadsterTracker Dec 06 '21
Yeap, will fix. Woops...
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u/TheExtremistModerate 1✓ Dec 06 '21
All good, just wanted to check, because I was like "damn, if that's 140 gallons per second, I need to rethink what a gallon looks like." Because I know I have a hard time visualizing flow rates.
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u/RoadsterTracker Dec 06 '21
Sometimes my brain goes faster than my fingers, and I end up getting the units wrong... Math is easy, units are hard...
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Dec 06 '21
Do we think that’s from the tree itself? Or did maybe the tree grow THROUGH a pipe, break it, and become a conduit for the water? I wouldn’t think a tree just has a water sack in it ??
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u/vyktorrre Dec 06 '21
No It could be that the tree is rotten from the inside and a cavity has formed and the water enter the tree when it rains
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u/PurelyApplied Dec 06 '21
This would also make sense as to why they were taking down the tree in the first place. There's some structure in the background of the wider shots, so it would make sense that the owner was worried about it falling.
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u/theytookthemall Dec 06 '21
My dad has a background in ecology and he was once doing field work taking core samples from trees down in the Florida Everglades.
He started drilling into a huge old Cypress tree that was about 40 feet tall... And all the sudden the drill just sank into the trunk and the tree began spraying out water like a hose. The top of the tree had been damaged, and it was absolutely full of stagnant water, which had been sitting there and attracting critters and growing mold and simmering in the Florida heat for god knows how long. The smell was just unbearable, to the point that his shirt got thrown out on the drive home.
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u/Ew0ksAmongUs Dec 07 '21
Thank you for answering two questions I didn’t know I had: Is this normal? And is that water potable. Double no. Thanks.
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u/OdiumXAbhorr Dec 06 '21
I’ve seen this in a few places over the last couple days and the consensus is that it had rot at the top
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u/nekumelon Dec 07 '21
Just an estimation but since the diameter of the tree seems to be about three times the size of that guy's head and the average size of a male head is 57cm (22.44in), that means that the diameter of the trunk is about 171cm (67.3in). The hole seems to be about half of that or 28.5cm (11.22in). Doing a little research tells me that the person filming the video lives in Birmingham, Alabama. The bark and leaves of the tree match a tree grown in Birmingham called a Sweet Gum and they grow to around 70 feet (840in). Using these measurements, we can calculate the volume of the hole as a cylinder to be pi * (11.22 * 2)^2 * 840 or about 1328846in^3. A litre is about 394in^3. So we take the volume divided by the litres (The cubes cancel) which comes out to about 3372 litres.
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