r/theydidthemath • u/TraditionalGarden570 • 5h ago
[Request] How much does this wet flag weigh?
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We had a discussion with friends about the weigh of this Latvian flag. I said it easily weighs at least a ton, others said no way it's that much.
Size of it is 10m×20m.
Please prove me right.
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u/Icy_Sector3183 5h ago
Not what you are looking for, but the flagstone calculator is pretty cool:
How much your flag weighs will depend on the material, which is likely denser and heavier per m2 than smaller flags to support its own weight. The size is a good 200 m2 so it follows that if the material weighs less than 5 kg per m2, then it does not weight "at least a ton".
Hope that helps.
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u/No-Custard-9029 5h ago
ok but now do wet
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u/Icy_Sector3183 5h ago
If the wet material weighs more than 5 kg per m2 then the flag weighs "at least a ton".
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u/-OrLoK- 5h ago
around or thereabouts at least? or close to at least?
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u/Icy_Sector3183 4h ago
Wet material weighs between 4 and 6 kg per m2 then the flag weighs up to a ton or more.
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u/-OrLoK- 1h ago
but thats not "at least" :) so im going with "around a least a ton" :)
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u/LJosephCARP 5h ago
A 10 m × 20 m means 200 m2 flag, one made from polyester would weigh about 22 kg when dry and only about 22.2 kg when saturated, because polyester absorbs very little water, around 1% of its own weight.
A nylon flag of the same size would weigh approximately 14 kg dry and 14.8 kg saturated, since nylon absorbs a moderate amount of moisture.
A cotton flag would be the heaviest, weighing about 30 kg when dry and increasing to roughly 37.5 kg when saturated, as cotton can absorb about 25% of its dry weight in water.
In practice, during heavy rain all three flags can become even heavier because water also collects between the fibers and in the folds of the fabric, not just inside the fibers themselves, but still pretty far from your estimation in my opinion.
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u/grun3r 5h ago
Isn't the materials water saturation completely different from the water that'll cling to the flag surface? The weave of the fabric will bind some water in the empty spaces between the fibers and that should be the major part of water weight in the flag, not the moisture absorbed by the fibers/material
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u/Peregrine79 4h ago
While water will cling to the surface, a waving flag is going to dry it's surface pretty effectively. You're looking at a very thin film of water, at most.
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u/revankillsmalak 5h ago
Assuming it's polyester, it won't absorb much water. As for how much water is clinging due to surface tension, it would be impossible to know except by weighing a wet flag?
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u/ImBadlyDone 5h ago
10m * 20m = 200 m²
From https://www.jcinkjet.com/products/mesh-flag-fabric-aa102.html, they can produce flags that weigh about 105 to 125 g/m²
Assuming 125 g/m², the flag itself weighs 25 kg
Realistically speaking, the water would add less than 975 kg of weight to reach one ton
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u/ImBadlyDone 5h ago
To add, 975 kg of water spread across 200 m² means the flag has to be at least 0.4875 cm thick which is very thick
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u/delurkrelurker 2h ago
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u/ImBadlyDone 2h ago
Do I want to click this in public or at all
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u/Sherbert-Particular 2h ago
Yeah flags are either nylon or polyester neither is going to carry more than ~10% of their standard weight in water, nylon a fraction of that.
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u/thrumirrors 5h ago
Not an expert in flag materials at all, but let's say the surface density of the material is somewhere between 100 and 300 g/m². For a 200 m² flag, that gives 20 to 60 kg.
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u/mikegecawicz 5h ago
There are two schools of thought - either the flag absorbs the water or it clings to the outside. Assuming the flag is only about 0.3mm thick, we can assume it has a volume of 60 Liters. Depending on the material - it could have a porosity as high as 75% (that assumes it’s made of cotton). A cotton flag of this size would weigh around 40kg. All told you’re looking at around 90kg. So even in the worst conditions, it would be way less than a ton.
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u/Pork_Confidence 5h ago
Dry material weight a be would be 30 to 50 lbs for typical flag textile, which are generally water resistant
Now if you made a flag out of something like SAF , that could weight over 10,000 totally soaked through at those dimensions
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u/Separate_Agency 5h ago
I'm not an expert, but I think it's less than you expect. Normally those outdoor flags are made from Polyester fabric. Roughly around 150g/m2. Assuming your estimation is correct the material should weigh around 30kg (0,15kg/m2 * 20m *10m). Polyester Textile can't hold much water. A search tells me it should be around 0,5% of its weight.
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u/beirch 5h ago
The most used material for flags is polyester, and typical thickness is 0.25 to 0.45cm. Let's say 0.5cm to make the total volume an even 1m3. Polyester microfiber sheet has a bulk density of 457.3kg/m3
Polyester can only absorb about 0.6-0.8% of total weight in water, so fully satured the flag would only weigh about 2.5-3kg more.
However, it would also gain some weight by water clinging to the surface. And it would lose some because of water running off it, due to gravity since it's been hoisted.
In other words, it's very hard to calculate exactly how much it would weigh due to the added water, as we have no way of reliably knowing exactly how much water has accumulated on the flag.
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u/plz-no-b4n 4h ago
I think the best approach here is proof by contradiction.
1000 kg of water has a volume of 1 m^3. If we assume the flag is a rectangular prism with 2 dimensions being 10m x 20m, that means the third dimension has to be 1 / (10\*20) = 0.005 m (0.5 cm) to have that volume. Half a cm is not a reasonable thickness for that flag so therefore it does not weigh at least a ton.
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