Buoyancy question
February 22, 2017 2:33 PM   Subscribe

i want to put an inflatable pool in my small backyard. Then I want to fill it with water and lie on its surface on an inflatable chaise/raft thing.

I need the pool to be around 6 ft in one direction since I'm around 5 and a half feet tall. Which means the actual dimension of the pool (width or length if it's a rectangle; diameter if it's a round pool) would have to be around 7ft. because the inflatable side(s) is about 6" wide.

The question is, if I weigh around 150 pounds, how deep does the water in the pool have to be for me to float on top of it on the float and not sink? And is there a way to calculate this for other weights?

and does it matter if I get a rectangular pool that's 7 ft long x maybe just 4' wide? In other words, does the width dimension matter as well? Would I do better with a round pool 7' in diameter?

I'm looking for the calculation for my specifics but I'm also interested in how one calculates what the length, width, and depth of an enclosed body of water needs to be in order for a person of X number of pounds to float on it using an inflatable device (or without an inflatable device: what would be the difference if any?)
posted by DMelanogaster to Science & Nature (11 answers total) 3 users marked this as a favorite
The weight of water displaced will be equal to the force of your weight (68kg). That's Archimedies' principle. So you'll displace 68 litres of water (a litre weighs a kg), or 0.068 cubic metres.

A 7'x4' pool with a 6'x 3' inflatable in it has a water surface (around the inflatable) of 10 square feet, or 0.92 sq. m.

The displaced water increases the depth of the water in the gap around the edge of the inflatable. Dividing volume by area to get depth: 0.068 / 0.92 = 0.074m, or 7.4cm, or just under 3 inches.

Given that your weight won't be perfectly distributed across the inflatable, I'd go for a couple more inches of water to be safe.
posted by pipeski at 2:55 PM on February 22, 2017 [6 favorites]

A floating object displaces an amount of water equal to its weight. 150 lbs. of water is — back of the envelope — 4200 cubic inches. If your raft is 6 ft. (72 in.) long and let's say 3 ft. (36 in.) wide, it only has to sit (on average) less than 2 in. below the surface of the water. But the bottom of your raft probably isn't flat, and you need the lowest points, not just the "average" of the bottom surface, to be above the bottom of the pool, so let's say 4 in. if your raft is fairly stiff, more if it flexes.

The length and width of the pool doesn't affect whether you can float in it. You'll sink to the same depth below the surface of the water in a 73"x37" pool as you would in an olympic -size pool.

(I was about to add that the difference is that if you have a pool which is barely deep enough you'd have to fill it to the rim, and then some would slosh over the edge when you got in, and if you got out then back in you'd have to refill it. But on further reflection, that was incorrect: the amount left in the pool after some sloshes over the edge from the first time you got in is still enough to float you again. The 4" water depth needed includes any rise in the water level due to displacement when you get in, so you'd be OK.)
posted by DevilsAdvocate at 2:56 PM on February 22, 2017

Water weighs 62 pounds per cubic foot. Archimedes teaches us that the buoyancy force exerted on the raft is equal to the weight of the water it displaces, which means that you, at 150 pounds, will displace 2.4 cubic feet. (150/62)

Divide that volume by the length and width of the raft to get the depth that it will sit in the water. So, for a 7x4 raft, 2.4/7/4 is 0.08 feet, or just over 1 inch.

The vessel needs to be at least a little bit bigger than the raft, or else you just sit on top of it, like a hydraulic piston in a cylinder.

The raft is a little flexible, though, so I'd build in a safety margin there.
posted by Huffy Puffy at 2:56 PM on February 22, 2017 [1 favorite]

Keep in mind that one of those chaise things will have you sitting partially upright so you may be able to get away with something 6' around.
posted by jessamyn at 2:59 PM on February 22, 2017

On reflection, my answer was a bit roundabout.

All you really need to do is divide your weight in kg by the area of the inflatable in square metres, then multiply by 10. That give you the depth the inflatable will sink to in centimetres, assuming a uniform load.

The size of the pool only determines how much the water rises. Climb into a bathtub and the water rises a lot. Jump into the sea and it won't (much).
posted by pipeski at 3:11 PM on February 22, 2017 [2 favorites]

Everybody else is doing a great job with math but as a person experience in sitting on my butt in pools, you need to find your raft first and then ask this question. A cheapo dollar store raft is going to sit differently (likely with your legs off the side and almost seated because it's cheap and too narrow so you start to tip if you're totally on it) than a better quality one that's a little wider but you'll actually float or a mesh one which has you float a lot less but is very relaxing and cooling.

What you really need to do is get the raft, then jump in a friend's pool (or one at a gym or something) see how much you dip below the water line at your lowest point (likely the hips but it depends on the person) and go from there.
posted by raccoon409 at 4:52 PM on February 22, 2017 [7 favorites]

You've got a couple great "assume a spherical cow" answers, but practically I think unless you do something like raccoon409 suggests your butt is going to hit the bottom.
posted by achrise at 5:19 AM on February 23, 2017 [1 favorite]

Thank you for the answers. I don't have a friend with a pool, and no gym pools in my life allow you to use a raft.

I was astonished to read answers like 3". The depth of the smallest pool I was considering is about 18". So it sounds as if I'm safe to assume that, in a pool 7' long and 4' wide and 18", this human WILL FLOAT.

raccoon409, thank you for the mesh float suggestion (or at least a better-quality float).
posted by DMelanogaster at 6:22 AM on February 23, 2017

Hey, you know what? In my experience, when you lay on a raft, the top of the raft never lays below the water surface. (It can fold up and partially submerge when you get on/off, but then it flattens back out.)

So look at the thickness of the raft, and just make sure your water is deeper than that.
posted by Huffy Puffy at 7:06 AM on February 23, 2017

So it sounds as if I'm safe to assume that, in a pool 7' long and 4' wide and 18", this human WILL FLOAT.

A raft that gets 18 inches down is the opposite of floating.
posted by HiroProtagonist at 5:53 PM on February 23, 2017

Follow-up: on an inflatable raft with my pool filled around 12" deep I float great, but I don't love the experience because I'm not at all in contact with the water. On a spring float, where I was hoping to be slightly below the surface, I sank to the bottom!! Any ideas why?? Also I can't use a "noodle" because, again, I sink like a stone.

I feel like this.
posted by DMelanogaster at 11:47 AM on July 9, 2017

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