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Post 53A – Calculating Buoyancy of a piece of PVC Pipe.

UPDATE: I have added several new posts with a better way of creating a raft. PVC Pipe would be an expensive way of getting the job done, Plastic Barrels would be much much cheaper.

Please check out the following four posts.
A Plastic Barrel Pontoon Raft Part 1

A Plastic Barrel Pontoon Raft Part 2

The Final Analysis of a Floating Barrel

The September Equinox and Look at what I just found!  (Someone is creating barrel rafts commercially.)

Click on the image to see a larger view.

After looking a little closer at the Hammock Boat picture, I noticed the pontoons seem to be made out of PVC pipe.  So I decided to do a little bit of calculating to determine what kind of force we could get using PVC pipe for pontoons.   My first guess was to try 3″ PVC,,,, My guess was wrong as you shall see.

However, not all is lost. Just some time was used and that is a whole lot better than try it and see what happens because everything would have been lost.  As the old statement goes: “Back to the drawing board.”  This is an opportunity to show how I did the calculations.  We will be using the picture shown in this blog.  I want to point out a feature this web posting software does.  If you click on the image it will display a large view of the image.  To return back to this post use your browser previous page arrow.

Step 1:  I looked up the dimensions and weight of both 3″ and 4″PVC pipe.  These are:
3″ PVC — Outside Diameter = 3.5″, — Weight is 1,41 lbs per foot
4″ PVC — Outside Diameter = 4.5″, — Weight is 2.01 lbs per foot.

Step 2: I looked up the density of water and at 70 deg F, water weighs 62.3 lbs per cubic foot.  We will be working in inches.  1 cubic foot = 12 X 12 X 12 = 1728 cubic inches. Dividing 62.3 / 1728 gives the density of water to be 0.0361 lbs / cubic inch.

We will look at the cross section area of the pipe and determine the area displacing water.  This will be multiplied by 12 to calculate the volume of water being displace by a foot of pipe.  From that we can determine the buoyancy developed on the pipe by the weight of the water being displaced.  We can then subtract the weight of the pipe to determine the amount of lifting force developed.

Refer to the picture to understand the calculation method used.  First, I drew a lines at 1/2″ increments from the bottom of the circle.  These are used to determine the displacement of water as the pipe is lowered in the water.  I then used CAD to draw a radius line from the water line on the outside of the pipe to the center of the circle. While just the bottom of the pipe is resting on the water the water being displaced is the area between the outer edge of the circle.  The way we will determine that is we will calculate the percent of the whole circle area the “pie slice” will use.   Then we will subtract from that “pie slice” the triangle above the water line.  The remaining area of the pie slice will be the displacement area.

The area of a circle is found by the formula = pi * r * r (r squared).  In the case of the 3″ PVC pipe (3.5″ circle) this is 9.62 square inches.

The following is the example shown in the picture.
The pipe is “sunk” 1/2″.  The angle as found by CAD is 88.83 degrees.  This means the pie wedge takes up  88.83/360 or 0.247 of the full circle area.  0.247 X 9.62 = 2.37 square inches.  CAD was then used to find the area of the triangle above the dashed line.  This was 1.53 sq. in.  2.37 – 1.53 means an area of 0.844 was below the waterline.  0.844 X 12 (one foot) give 10.13 cu. in of displacement.  10.13 * 0.036 lbs / cu. in. gives us the weight of the water displaced = 0.365 lbs.    The actual upward force developed = 0.365 – 1.42 (the weight of the pipe) = -1.054 lbs per foot of pipe.   This means the pipe will float deeper than 1/2 inch.

The calculations for various depths give the following results.
1″ deep = -.439 lbs
1.5″ deep = 0.28 lbs
1.75″ deep (1/2 sunk) gives 0.66 lbs
2″ deep = 1.04 lbs
2.5″ deep = 1.76 lbs
3″ deep = 2.38 lbs
3.5″ deep (completely submerged) = 2.74 lbs

This means a 10 ft piece of 3″ PVC pipe will only float 27.4 lbs.  BACK TO THE DRAWING BOARD!

This was a complicated post.  I hope it is clear, but if there are any questions Please contact me.

Gary


 

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12 comments to Post 53A – Calculating Buoyancy of a piece of PVC Pipe.

  • Joe

    For those people who want to try PVC pipe, knowing that it can get expensive, think about this. A 4 inch pvc pipe 10ft long is about $22 @ Home Depot. If you take one pipe and surround it
    by six more you effectively triple the diameter. The volume displacement then is 4×3=12″ diameter. R2 x 3.14 x 12 = 1356 cubic inches divided by 1728 cubic inches per foot x 62lbs(water) x 10ft = 486 lbs. I read somewhere that when working with pontoon tubes you should only consider the capacity of one tube just in case all the weight was on one side of your boat. so two ten foot tubes of 12″inch diamter would run about $308. Im personally going to try making two tubes using 16″ diameter cut plywood ( 6 discs) held together with 3/4 pvc pipe 10ft long. Then epoxy a cotton skin around that frame and fiberglass after. Using the same calculations as above, this tube should have a capacity of 826 lbs minus its own weight.

  • Joshua

    Firstly, fantastic work. I’ve been trying to figure out how much volume is required for so much weight and you broke it down in layman’s terms… Almost lol. I’m a crayons and construction paper kind of guy so would you correct any errors I have.

    In extra simple terms: an object will float as much water as it displaces, minus the weight of the object. So, 1 gallon is 231ci, which weighs 8.3lbs. So for every gallon displaced, you can float 8.3lbs, minus weight of material of course. But where I got lost was your depth/weight measurements. At 3.5″ deep, I came up with the same number, but if you submerge to 1.75″ deep, being half the depth and half the displacement, shouldn’t it also be half the weight? So instead of .66lbs that you have listed, shouldn’t it be 1.37lb? My concern for that is I feel the pipe/boat would be most effective submerged no more the half way. So that would mean, in my mind, instead of calculating weight for a 200lb guy and having it fully submerged, I should just figure the weight to be 400+lb bringing to the halfway point or higher.

    Thank you in advance for any and all help and for taking the time to write this up, it has been very informative.

    • Gary

      Hello Joshua:

      Several things here:
      First your quick and easy method of calculating completely submerged for a 400 Lb guy and building it for a 200 and having it 1/2 way submerged is a nice simple way to do it.

      In general, Numbers and Calculating and “math models” are really nice but everything is based upon assumptions so all that high-tech razzle dazzle only gets you closer that you would be otherwise… there is always a gotcha waiting in the wings somewhere. (example… the wood you build the frame out of gets wet and ends up weighing 2 times what you had figured or someone buys the beer in bottles and not cans…. etc. etc. etc.)

      As I wrote up this post I was unpleasantly surprised about how big the PVC pipe would have to be. I would have guessed at 3 in pipe at the max and it ended up being more like 6 in pipe. I then for my own curiosity looked up the prices for that pipe and the end caps and knew right then I would never build one of these. If you search my site you will find where I do the same calcs with a 55 gallon plastic barrel…. MUCH MUCH Cheaper! Also I have a video on there of a commercial company building floating docks, barges, and pontoon boats out of those. If you are wanting something in-between, look into a 35 gallon plastic barrel. That way you could have two side-by-side for stability and it would not be submerged very much.

      Now for the heart of your question. The reason it has very little lift at 1/4 submerged is the pipe is getting fatter as it is submerged more and more until it reaches the 1/2 way point.

      Imagine 4 guys want to split a pizza evenly, but instead of cutting it in the customary wedges they do 3 cuts. The first cut is right down the middle and then the second 2 cuts are parallel to the first cut but 1/2 way between the 1st cut and the edge of the pie. The two guys getting the crusty pieces are going to be very very ticked off about getting ripped off by the 2 that got the center pieces because they got much less pizza.

      That was the whole reason I did the trip into trigonometry just to accurately predict the size of the sliver that was submerged.

      Next step…. calculate the buoyancy of a beech ball. (Just kidding…. I don’t feel like taking that one on.)

      Have fun with it… and remember take your water wings with you when you try it out.

  • […] Calculating the Buoyancy of a piece of PVC Pipe – Archimedes principle of buoyancy is used to calculate the lift that can be developed by a piece of PVC pipe laying in the water using graphical methods. […]

  • […] Calculating the Buoyancy of a piece of PVC Pipe – Archimedes principle of buoyancy is used to calculate the lift that can be developed by a piece of PVC pipe laying in the water using graphical methods. […]

  • […] Calculating the Buoyancy of a piece of PVC Pipe – After looking a little closer at the Hammock Boat picture, I noticed the pontoons seem to be made out of PVC pipe. So I decided to do a little bit of calculating to … […]

  • […] Calculating the Buoyancy of a piece of PVC Pipe – Archimedes principle of buoyancy is used to calculate the lift that can be developed by a piece of PVC pipe laying in the water … buoyancy developed on the pipe by … […]

  • Brendon Killough

    I was planning on using 3″ pvc for a canoe stabilizer. If i put the stabalizer farther from the canoe, won’t it make the stabalizer more effective, and not needing to be anymore buoyant due to the leverage?

    • Gary

      Yes you are correct. How far and how much I do not know. There are tests you could probably do but those are probably no more effective than simply trying it and see what happens.
      Try any experiments in shallow water until you are sure of what you have created.

  • Thank You very much.. I was thinking if ever it would leaked that means water get in and you will lose more buoyancy, The Styrofoam will just keep the water away and I’m sure it will still keep the PVC pipe afloat. In my case, I inserted Mineral water canister that fits exactly and it weighs less than the foam. I just hope it wont break, cause Im planning with my DIY waterbike a long trip whenever its finished. I’m just halfway now.

  • Hello, What if you will fill it full of styrofoam? will the bouyancy change? Thank You.

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