One Mile long hose - Science, Math and Philosophy Forum

Check my math please.

A one mile long 1/2 inch hose would weigh 21,597 pounds?

Volume = Pie * r^2 * h = 3.14159 * .5^2 * 5280 * 12 = 49762.83 cubic inches of water.

Water weighs .434 pounds per cubic inch.

49762.83 * .434 = 21,597 pounds.

I am having trouble believing that answer.

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08-13-2022 , 07:13 PM

golddog

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Volume of a cylinder seems right. Only problem is the radius of a 1/2 inch hose is .25 in, not .5. (Besides the auto-correct of "pi"

)

I get ~12440 in^3 from that. Going to assume your weight is right, so ~5400 lbs of water.

Don't forget the weight of the hose, though, too.

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08-13-2022 , 07:21 PM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

A hose isn't a hose filled with water and you haven't mentioned whether you have a 0.5" ID hose or a 0.5" OD hose. Without more specifications, no calculations are warranted.

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08-13-2022 , 08:27 PM

JayKon

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Quote:

Originally Posted by golddog

Volume of a cylinder seems right. The only problem is the radius of a 1/2 inch hose is .25 in, not .5. (Besides the auto-correct of "pi"

)

I get ~12440 in^3 from that. Going to assume your weight is right, so ~5400 lbs of water.

Don't forget the weight of the hose, though, too.

That seems right, thanks. As to the hose itself, that would b somewhere between 1,000 and 2,500 pounds, depending on the exact hose.

The next question is what is a reasonable lift capacity for an electric drone (power fed by wires attached to the hose getting power from a generator on a truck)?

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08-14-2022 , 03:15 AM

PairTheBoard

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Quote:

Originally Posted by JayKon

Water weighs .434 pounds per cubic inch.

A cubic inch of water weighs nearly half a pound?

PairTheBoard

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08-14-2022 , 08:44 AM

Didace

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I believe Germany made use of heavy water in WWII.

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08-14-2022 , 11:51 AM

golddog

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Quote:

Originally Posted by PairTheBoard

A cubic inch of water weighs nearly half a pound?

Good point, that can't be right. As they used to say, "A pint's a pound, the world around."

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08-14-2022 , 12:08 PM

lastcardcharlie

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Not in the Commonwealth it isn't.

Quote:

One US liquid pint of water weighs 1.04318 pounds (16.6909 oz), which gives rise to a popular saying: "A pint's a pound, the world around".

However, the statement does not hold around the world because the British imperial pint, which was also the standard measure in Australia, India, Malaya, New Zealand, South Africa and other former British colonies, weighs 1.2528 pounds (20.0448 oz), giving rise to the origin of a popular saying used in Commonwealth countries: "a pint of pure water weighs a pound and a quarter".

https://en.wikipedia.org/wiki/Pint

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08-14-2022 , 12:18 PM

PairTheBoard

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Google says,

"One cubic inch of water weighs 0.036127 of a pound."

PairTheBoard

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08-14-2022 , 03:36 PM

#10

stremba70

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One cubic inch is 2.54^3 = 16.39 cubic centimeters. One cc of water is very close to 1 gram. 1 pound is 454 grams, so 16.39 grams is 16.39/454 = 0.036 lbs. It looks like the posted value from Google is right, or at least close enough.

The volume of water on a 1/2 inch ID hose with a length of one mile was correctly calculated above as 12440 cu in. The weight is therefore 0.036 x this volume or about 450 pounds

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08-15-2022 , 12:09 PM

#11

JayKon

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OK, so the correct calculation would be:

Volume = Pi * r^2 * h = 3.14159 * .25^2 * 5280 * 12 = 12,440.7 cubic inches of water.

Water weighs 0.036127 pounds per cubic inch.

12,440.7 * 0.036127 = 449.4 pounds.

Interesting that the lightest hose is twice the weight of the water.

Thanks guys.

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08-15-2022 , 01:17 PM

#12

PairTheBoard

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Quote:

Originally Posted by JayKon

If the inner diameter is 1/2 inch and the outer diameter is 1 inch then the outer section has three times the volume as the inner section. The area of a circle as a function of the diameter is a parabola. A = pi*(d/2)^2

PairTheBoard

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08-17-2022 , 10:52 AM

#13

Kalaea

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Join Date: Apr 2021 Posts: 493

Quote:

Originally Posted by JayKon

Half a ton plus per mile?

That's 630 lb for a mile of 5/8". prob closer to 500lb for 1/2", and that's without searching for the lightest hose.

Last edited by Zeno; 08-17-2022 at 11:02 AM. Reason: Deleted embedded ad.

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08-17-2022 , 11:24 AM

#14

JayKon

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Quote:

Originally Posted by Kalaea

Half a ton plus per mile?

That's 630 lb for a mile of 5/8". prob closer to 500lb for 1/2", and that's without searching for the lightest hose.

A 100' lightweight hose (including brass connectors) weighs 4.93 pounds.

5280 / 100 * 4.93 = 260.3 pounds.

So, you are correct, thanks.

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08-21-2022 , 08:22 AM

#15

Kalaea

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Apparently heavy lift drones can carry 200kg or about 440 lb. So you would need 2 or more likely 3 working together to lift the hose and water.

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08-21-2022 , 12:17 PM

#16

JayKon

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Quote:

Originally Posted by Kalaea

Apparently heavy lift drones can carry 200kg or about 440 lb. So you would need 2 or more likely 3 working together to lift the hose and water.

I don't think that would be appropriate. The weight, while a significant point, is not everything. There is the matter of sag in the hose, similar to the sag you see in power lines. I have a strong suspicion that there is a maximum length between drones to keep that manageable. Something like 50-250 feet.

This would significantly decrease the lift requirements of each drone, but adds the complexity of controlling multiple drones in series - a problem that should be a simple case of the sky drone displays that have been around for a few years now.

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08-22-2022 , 09:41 AM

#17

Kalaea

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I was thinking straight up. If you want the hose horizontal, it is a more difficult problem, yes. Probably not possible for drones, as only the end two (or end two groups) can apply horizontal force to keep the cable extended.(edit - not correct, all but the centre drone can apply sideways force to keep the hose taut). You'll also need to consider the tensile strength of the hose.
Thinking about it, I'm not sure the distance between drones matters for a flexible hose, except for reducing the sag depth.
May be possible with a rigid hose, but that will be heavier.

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08-22-2022 , 02:33 PM

#18

JayKon

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It seems unrealistic to keep the hose horizontal, some sag seems inevitable. Since I'm thinking about using this to put out grass fires, it is an outdoor use and therefore it would be better to keep it off the ground.

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08-22-2022 , 03:13 PM

#19

golddog

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Grass fire in an open area, or with trees around?

If the former, I wonder if you could rig up something like those big irrigation systems they have in more arid regions.

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08-22-2022 , 08:22 PM

#20

JayKon

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My thought involves something that would be fitted into a truck that could respond to a remote location. In the truck would be the hose, drones, water tank and maybe a foam tank (to require less water).

Oh yes, the hard part, a control mechanism such that a single person could operate it.

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08-23-2022 , 11:16 AM

#21

Kalaea

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Join Date: Apr 2021 Posts: 493

You're not going to get enough pressure through a mile of half inch tube to put out a cigarette, let alone a grass fire. Pressure drops rapidly with bore and length.

Why not just use drones with water tanks? Five heavy lift drones will carry a tonne of water, and will be able to deliver it to the fire site faster and in greater volume per minute than a hose.

edit - to get 8 lpm (2 gal/min) output you need 26 bar input pressure assuming perfectly smooth pipe or around 360 psi.

Last edited by Kalaea; 08-23-2022 at 11:31 AM. Reason: added pressure requirement

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08-23-2022 , 11:36 AM

#22

Kalaea

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Quote:

Originally Posted by JayKon

I think foam is made at the nozzle. You certainly can't pump foam efficiently under high pressure and long distance, it will separate into carrier gas and liquid.

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08-23-2022 , 11:38 AM

#23

JayKon

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Well, as it happens I have thought about that. Consider that wires need to connect from the truck to the drones to power them (batteries don't have enough energy density). That could also provide power for small assist pumps along the way.

Also, fire engines have pumps that can deliver high pressure in a 4-5 inch hose 50 feet in the air.

Do you have the formula for pressure, bore and length?

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08-23-2022 , 11:46 AM

#24

JayKon

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Quote:

Originally Posted by Kalaea

I think foam is made at the nozzle. You certainly can't pump foam efficiently under high pressure and long distance, it will separate into carrier gas and liquid.

Yes, it is. However, the feed line for the material can be much smaller.

Remember, this is an idea I'm trying to flesh out enough to get someone else to do.

Also, I no longer think one mile of hose would be required. The distance would be something along the lines of what an operator could see - say 1,000 - 2,000 feet.

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08-23-2022 , 03:03 PM

#25

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

The problem is that the static forces (gravity) will be negligible compared to the dynamic forces. Hoses spraying significant quantities of liquids seem to really enjoy whipping around.

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