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Mathemtic Formula for Tubes

Mathemtic Formula for Tubes

Mathemtic Formula for Tubes

(OP)
I'm looking for a formula that I could use to find out how many .013" diameter wires can fit into a .75" ID pipe. I realize that we cannot divide the area of the pipe by the area of the wire, that give us the number we could fit in with the pieces over lapping. Is there a calculus or a algebraic formula out there that can be applied to this? Any suggestions would be greatful.

RE: Mathemtic Formula for Tubes

Per the National Electrical Code the total area of cross sections of conductors shall not exceed 40% of cross section of conduit. The NEC has tables and typical info on wires and conduits to make it easier.

RE: Mathemtic Formula for Tubes

(OP)
i should have been more specific. we are trying to place as many of the wires into the pipe as possible. they are going to be held in place with wax and then have their ends ground down to a specific length. they are not to be  used for anythiny electrical.

RE: Mathemtic Formula for Tubes

BMccarthy81 - I had to solve this same problem for a project over 30 years ago! In our case, it  was much simpler since we had to determine the maximum number of 1/8" OD dia. pipes that would fit inside a 1" ID dia. pipe. I solved it by trial and error, but co-worker discovered that there ARE formulas for such things - unfortunately I don't remember what they are called.

However - this web page "looks" like it may provide enough information to work out to your situation
http://mathworld.wolfram.com/CirclePacking.html

Best Wishes

p.s. When you find out, please let us know.

www.SlideRuleEra.net

RE: Mathemtic Formula for Tubes

You may try to solve the problem in parts.
Named X as the internal diameter of the pipe.
Named Y as the external diameter of the wire.
To form the first layer of threads leaned in the internal walls of the tube, you will need Z1 numbers of threads.
Z1= integer {[(X - Y/2) x 3.1416]/Y} = 179
You will now be able to imagine that possesses a new diameter tube X1 with value of X less 2 times Y.  
Consider the integer number of the division of X for Y (call this as result of n). In this case is 28.
Repeat the procedure n times to obtaining the Z2,Z3... to Z28.
The sum of Z1 to Z28 plus 1 (the center) will be the wanted result.
Z = integration of (Z1 to Z28) + 1
Zn = integer {[(Xn - Y/2) x 3.1416]/Y} where Xn= X - n times Y.

RE: Mathemtic Formula for Tubes

Sorry !
The last correct sentece is:
Zn = integer {[(Xn - Y/2) x 3.1416]/Y} where Xn= X(n-1) - n times Y.

RE: Mathemtic Formula for Tubes

Layer    D    D-13    +(D-13)*Pi/13    Wires No.
1    750    737    178.10414    178
2    724    711    171.8209546    171
3    698    685    165.5377692    165
4    672    659    159.2545838    159
5    646    633    152.9713984    152
6    620    607    146.688213    146
7    594    581    140.4050276    140
8    568    555    134.1218422    134
9    542    529    127.8386568    127
10    516    503    121.5554714    121
11    490    477    115.272286    115
12    464    451    108.9891006    108
13    438    425    102.7059152    102
14    412    399    96.42272979    96
15    386    373    90.13954439    90
16    360    347    83.85635899    83
17    334    321    77.57317359    77
18    308    295    71.28998819    71
19    282    269    65.00680279    65
20    256    243    58.72361739    58
21    230    217    52.44043199    52
22    204    191    46.15724659    46
23    178    165    39.87406119    39
24    152    139    33.59087579    33
25    126    113    27.30769039    27
26    100    87    21.02450499    21
27    74    61    14.74131959    14
28    48    35    8.458134192    8

total    2598 wires of 0.013" in a 0.75" pipe.

RE: Mathemtic Formula for Tubes

(OP)
Thank you all for getting back to me. I found out that the "circle packing" or "sphere packing" method is the best way to find out how many actual pieces of an OD wire into a specific ID of a pipe. The most efficient way to pack cirlces is a hexagonal pattern, six cirlces around on circle. The french mathematician found out this from studying bee hives, and investigating the shape of the honey-combs. His theorm was proven in the 1950's. It turns out that the cirlces use up about 90% of the actual area.
Wehave records of packing wire into tubes, the amount and their diameter. From the field tested method we found that we were using 85-87% of the pipes area. We were able to figure out a ball-park amount, and quoted the needed job.

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