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There exists a single solitary tree at the mouth of a small river. This tree is basically a fountain of youth, granting immortality to anyone who eats it's grapefruit-sized fruits.

As you can imagine, such a tree is gigantic; so big that it's water requirement completely absorbs the discharge from the river which runs directly to it.

Just how large is this fruitbearing tree?

Assume:

  • The stream flows at 100 cubic feet per second
  • Fruit is comparable to grapefruit
  • Tree structure and leaves are similar to a red oak
  • All other nutrients, co2, sunlight, etc. are abundant
  • The wood is 3x stronger than A36 steel
  • Climate comparable to US Hardiness Zone 6
Acumen Simulator
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    Insufficient data for a meaningful answer. It depends on the tree, on how long the tree has been there, the type of fruit it bears, the size of its leaves, the size of the tree. – Separatrix Dec 12 '17 at 14:43
  • @separatrix if I knew the size of the tree I wouldn't be asking the question? =) I'll update... – Acumen Simulator Dec 12 '17 at 14:44
  • It might be a slightly above average palm tree or a vast plane or fir tree. – Separatrix Dec 12 '17 at 14:46
  • @separatrix thanks, corrected to represent more accurately the size of the stream I was envisioning. – Acumen Simulator Dec 12 '17 at 14:59
  • After your last edit I think the only thing missing is climate – Separatrix Dec 12 '17 at 15:04
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    For a [tag:hard-science] declarations like "The wood is 3x stronger than steel" are extremely vague. There are at least three parameters that can be called "adjective strength", with totally different meaning. – Mołot Dec 12 '17 at 21:55
  • @Mołot was thinking tensile, shear, and compression... what would be a more appropriate tag? – Acumen Simulator Dec 12 '17 at 21:59
  • I'm not saying you have to retag. I'm only saying that if you require precise mathematical calculations, you should be precise and detailed in your question in the first place. And given the really, really wide range of steel parameters, it would be much better if you would just give strength parameters as numbers and respective units. – Mołot Dec 13 '17 at 00:23

3 Answers3

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Some quick googling shows a tall Oak may use 50 gallons of water in a day. 100 cubic feet per second gives you over 500 gallons of water per second - again, from a quick search (700-ish if they're metric gallons, 600-ish if they're imperial gallons).

To consume and disperse that amount of water into the air the tree would need to be 864,000 (10 x 60 second * 60 minutes* 24 hours) times the volume of a large 80 foot tree, giving a tree approx 7,600 feet tall with canopy of similar width.
(Assuming Oaks are as wide as they are tall, so I cubed 80 to get the volume, multiplied by 864,000 and got the cubed root of that).

And actually that's a minimum size.

So a tree over a 2.3 kilometers (1.4 miles) high with a canopy as wide.

... though it must be noted a tree that massive defies the laws of physics, see How tall can a tree grow

Binary Worrier
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    Can a tree that high still transport water? I'm no expert in trees, but I imagine one has to go wide not tall – Raditz_35 Dec 12 '17 at 15:13
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    I seriously doubt it, but I have no knowledge of the limits of such things, but the result of my back-of-an-envelope type calculation gives a tree of such proportions. – Binary Worrier Dec 12 '17 at 15:14
  • It seems I misread that article, it's more like 50 gallons per day, I'll fix yup those calculations. – Binary Worrier Dec 12 '17 at 15:30
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    A tree that tall cannot transport water. See https://worldbuilding.stackexchange.com/questions/10793/how-tall-can-a-tree-grow – kingledion Dec 12 '17 at 15:39
  • This seems intuitive, even though large numbers are large. This would put the trunk at about 600ft diameter! Does the fruit not factor into size? or is it negligible? – Acumen Simulator Dec 12 '17 at 17:15
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Water consumption is not directly relatable variable to tree size

Tree size, adaptations, and environmental conditions govern a trees water consumption.

Environmental conditions and adaptations in particular, one reason trees lose water is to cool themselves down in order to photosynthesize efficiently however this is dependent on its adaptations. This is what makes the difference between a cactus and a mangrove.

Quora claims a mature Oak can go through 200 gallons a day

I bothered to do the math:

your tree needs to consume roughly 648,000 gallons of water in a day. Im all for the stretching the limits of biology but that doesn't sound possible for your select biome. That tree would be making clouds like a rainforest.

matter of fact to put this in perspective:

  • 1 inch of rain over an acre is equivalent to roughly 27K gallons of water
  • an acre of rainforest usually receives roughly more than 100inches of rain a year

your tree needs to consume roughly 30 times what an acre of rainforest can process not even absorb. (bare in mind I intentionally generalized some numbers in there like 100 day years)

The theoretical maximum for a trees height is posed roughly at 125M. This is posed as the theoretical maximum because it is as high as scientists believe a tree can carry water to its top overcoming the force of gravity. This is also close to what redwoods can achieve.

Since I do not have enough the figures necessary to answer this question I will build the equation.

This super tree has not provided a mechanism for overcoming the scientific heath maximum even though height doesn't correlate directly to water consumption. So max height of this tree is roughly 125M.

  • Water consumption is more closely related to the surface area of the canopy with tie ins to its density. Depending on how diverse it is in photosynthesis. The number needed here is water needed to support 1 sq unit of photosynthesizing canopy assuming trunk and limb water consumption is negligible. This number can be determined by finding the water consumption of a leaf and multiplying that by the possible number of leaves in a sq unit of canopy.

  • with that number you divide the water needed to consume by it to determine to find your total surface area of canopy which is also related to the ~width~ of your tree.

This tree would probably be like pando having many trunks over acres that look like trees.

anon
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  • so its root system would be roughly 30 acres? – Acumen Simulator Dec 12 '17 at 17:42
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    That was how much water an acre of rainforest receives not uses. And you have to account for rainfall and subterranean water sources when talking about areas that big. This tree would need foliage covering more than 30 acres – anon Dec 12 '17 at 17:49
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    At this rate a tree such as this could transform Saharan desert into a forest simply by putting a portion of that much water into the air – anon Dec 12 '17 at 17:54
  • You might start considering Pando at this point https://en.wikipedia.org/wiki/Pando_(tree) – anon Dec 12 '17 at 17:58
  • Not sure I am following the turn desert into forest claim... I'm calculating that 648,000 gal of water can be stored in a 2180ft cube of air @ 50*F. Not to mention a 5mph wind would change over the air 10 times an hour. Unless I calculated incorrectly. – Acumen Simulator Dec 12 '17 at 18:00
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    that claim is speculative as there is no way to know what the environment will do with that water vapor, though I reason a dusty environment like the sahara would precipitate that somewhere daily. Be it dispersed to form grasslands, concentrated to form forests or some how dissipated all together. The point of that comment is at that scale it would literally be influencing its surrounding ecosystem. – anon Dec 12 '17 at 18:19
  • true... it is quite a lot of dispersion nonetheless. I like the pando idea; maybe max feasible size as female in center with male pando surrounding several acres would be more 'realistic'. – Acumen Simulator Dec 12 '17 at 22:04
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Behold the Great Banyan. Great Banyan http://plantcellbiology.masters.grkraj.org/html/Plant_Cellular_Physiology8-Loss_Of_Water_II-Transpiration.htm

1 tree. 3.7 acres.

I here assert that with this mode of growth a single banyan could spread to cover an enormous area. Now how big would a single tree of this sort be to deal with the water flow you propose? Let us assume all water is lost, eventually, as transpiration.

From the same source: a 1 acre piece of forest transpires 20,000 liters/day.

Your river delivers 100 cubic feet/second. That is 2800 liters/second. x 86400 seconds in a day is 241,920,000 liters/day. Divided by 20,000 L/acre = 12096 acres.

Pando is a single clonal tree expansion: 2 orders of magnitude bigger than the great Banyan at 106 acres.

Your tree is 2 orders of magnitude larger yet at 12096 acres. But that is only 48 square kilometers. The Okavango delta is much larger, at 6000 to 15000 square km, and it does not empty into any lake or the sea. All of its water is ultimately evaporated or transpired.

Okavango delta from https://voices.nationalgeographic.org/2014/06/21/unesco-world-heritage-committee-vote-on-okavango-delta-today/

A spread out swampy waterway like the Okavango delta ending in a sprawling "tree" like one of those described above would be a way to fill the criteria you set out.

Willk
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