Sometimes I get so intent on figuring out a problem, I do a lot more than is necessary. In Post 53A, I showed a graphical method of calculating the buoyancy of PVC pipe and tried with a 3″ pipe. I found it would not get the job done. This time around I wanted to do the same problem with a spreadsheet so other sizes of pipe could quickly be calculated. After going through all of that, I realised that all I really needed to do was calculate with the pipe 1/2 immersed and fully immersed to get an idea of the amount of lift the pipe can provide. Those calculations are easy to do – the area of a circle, and 1/2 that amount.

The summary of those calculations are shown here. Currently, I would figure on 6″ PVC with two on either side of the Hammock Stand as shown in the picture for Episode 53.

However, since I have already done the work this post is a good opportunity to show how to use a spreadsheet for design calculations.

Refer to the first picture. The way we will calculate the lift provided by the pipe when it is immersed less than one-half way is to do the following.

- Determine the angle A, from the center of the pipe to the immersion level. This is done by taking the arc-cosine of (radius – depth)/radius)
- Determine the area of a the pie slice that is 2 X angle A wide. This is done by multiplying the area of the full circle X 2 X A / 360.
- The immersed area = the pie slice area – the triangle area of the pie slice above the water level. The area of the triangle is 1/2 the base X height of the triangle. This is radius X sine(A) X (radius – depth).
- Once the immersed area is found (the red area on the picture) this is multiplied by 12 to get he cubic inches of displacement per foot of pipe. This is then multiplied by the density of water per cubic inch (0.0361 lb / cu in), to determine the gross lift. The weight of the pipe / foot is then subtracted to determine the net lift provided.

If the pipe is immersed over 1/2 the diameter, the calculations are similar, except the immersed area = full pipe area – pie slice area + the triangle area.

The spreadsheet used to do all these calculations can be found here: Displacement spreadsheet in Excel format ,& Displacement spreadsheet in LibreCalc format.

Gary

Please furnish the detail calculations

The calculations are described in the text of the blog post and are written in the formulas that are within the cells of the spreadsheet. WordPress is not really designed to show calculations. I really have only two other options. One would be to create a video showing how the calulations are stored witin the spreadsheet and the other would be to hand write out one example, scan it and post it as a download. My handwriting leave a little bit to be desired but I can do that if necessary.