Calculate a given weight of a rol copper

General
1

Hello Everyone,

Can you advise me with the follow :

I have to calculate the weight of a particular copper pipe based on the diameter and specific gravity.

I have a rol of 10 kg cupper pipe with an outer diameter of 0.64 m and an inner diameter of 0.30 meter. The pipe itself has a diameter of 10 mm and its specific gravity (weight) is 0.250 kg per meter.

Now someone ask for 3 kg cupper pipe.

We know the specific weight is 0.250 kg per meter.

The formula for calculate the exact length we need based on the specific weight is :

Diameter rol * 3.14 (pi)
0.64 * 3.14 = 2,0096 m (circumference of one full circle pipe)

To calculate the amount of circles pipe necessary :

Circumference one circle * specific weight
2.0096 m * 0.250 = 0.5024 kg for 1 circle

Now we know the weight of 1 circle, we can easily calculate the amount of circles with :
Requested weight / weight for 1 circle
3 kg / 0.5024 kg = 5,971337579617834
which mean :
5 full circles plus 0.97 m

So long so good. But as I mentioned the outer diameter is 0.64, and the inner is 0.30 m. Our formula works good as long as the cutted circles are close to the outer diameter (where we start cutting). But imagine that we need 7 kg which mean with the formula above, taking the outer diameter the error margin becomes too great. So we need to take an average diameter which is better but still not good enough. Copper is very expensive that is why the calculation have to be accurate.

My question to you :
Do you know a method to accuratelly calculate the requested amount of weight taking in mind the difference between the outer and inner diameter?

I really do hope I succeeded in showing you a clear picture of the problem.

Any ideas, formulas will be very much appreciated. I thank you in advance for your time and efforts spend on my request.

Wish you all a very nice day and all the best.

Friendly greetings,

Chris

2

Why do it like that in the first place???

That value would depend on where exactly on the diameter your pipe ends/starts (because it us not a circle, more like a snail)

Much better to calculate:

It is 0.25 kg per meter

I need 3 kg -> 12 meter of pipe (= 3/0.25 = 3*4)

I need 7 kg -> 28 meter of pipe (= 7/0.25 = 7*4)

That is precise and much easier to measure too.

3

[quote=167832:@Chris Verberne]Hello Everyone,

Can you advise me with the follow :

I have to calculate the weight of a particular copper pipe based on the diameter and specific gravity.

I have a rol of 10 kg cupper pipe with an outer diameter of 0.64 m and an inner diameter of 0.30 meter. The pipe itself has a diameter of 10 mm and its specific gravity (weight) is 0.250 kg per meter.

Now someone ask for 3 kg cupper pipe.

We know the specific weight is 0.250 kg per meter.

The formula for calculate the exact length we need based on the specific weight is :

Diameter rol * 3.14 (pi)
0.64 * 3.14 = 2,0096 m (circumference of one full circle pipe)

To calculate the amount of circles pipe necessary :

Circumference one circle * specific weight
2.0096 m * 0.250 = 0.5024 kg for 1 circle

Now we know the weight of 1 circle, we can easily calculate the amount of circles with :
Requested weight / weight for 1 circle
3 kg / 0.5024 kg = 5,971337579617834
which mean :
5 full circles plus 0.97 m

So long so good. But as I mentioned the outer diameter is 0.64, and the inner is 0.30 m. Our formula works good as long as the cutted circles are close to the outer diameter (where we start cutting). But imagine that we need 7 kg which mean with the formula above, taking the outer diameter the error margin becomes too great. So we need to take an average diameter which is better but still not good enough. Copper is very expensive that is why the calculation have to be accurate.

My question to you :
Do you know a method to accuratelly calculate the requested amount of weight taking in mind the difference between the outer and inner diameter?

I really do hope I succeeded in showing you a clear picture of the problem.

Any ideas, formulas will be very much appreciated. I thank you in advance for your time and efforts spend on my request.

Wish you all a very nice day and all the best.

Friendly greetings,

Chris[/quote]

Since obviously you calculate in circles, why not estimate the circumference according to the position to the center ? I do not know how many circles there are in a roll, but if there was 10, for instance, diameter would be depending on circle 0 for outer and 10 for inner :

30+(3.4*(10-circle))

That way instead of an average per roll, you have an average per circle, much more precise. You could even refine the method down to portions of circles.

Of course this means your very simple formula to calculate the number of circles no longer works. You got to add the weight of each circle and portion based on the circumference. Note that for a given type of pipe, the weight of a circle is always the same, so you could calculate it once and then make it a series of constants.

4

Is this somebody’s maths homework? :wink:

5

I’m missing something special about circles & cutting I suspect but … you say “We know the specific weight is 0.250 kg per meter.”
So 3Kg = 12 meters of pipe

No ?

7

I will cime in…

You didn’t tell us how precise you need the length of the pipe to be, how it is ordered in the rol, … so we can’t do but try to guess what you need. How long is the longest piece you would have to cut?

If it’s not too long I thought about a differet approach: you could insert a cable of known length (the length you need to cut, calculated as explained above by other people) inside the pipe the tip of which somehow tells you where to cut. A magnet attached to the tip of that cable can be detected by another magnet (or a compass) from the outside, for example.

There is something I would traslate into English as “electrician guide” (guia de electricista in Spanish, see images here: https://www.google.es/search?q=guia+electricista&source=lnms&tbm=isch&sa=X&ei=mj_hVIeOBoL3UIqWhLAJ&ved=0CAgQ_AUoAQ&biw=1366&bih=667#imgdii=_) that can serve that purpose.

Fun problem anyway, I hope you find a suitable solution.

Julen

8

The 0.25 kg is meters squared…first we need to find the actual volume and area which the copper itself occupies.

Calculating a given weight of a Cu Pipe

X = Density of Metal/Alloy
Y = Wall Thickness
Z = Outer diameter minus Wall Thickness (Y) (or simply Inner Diameter)

As an American, I can relate to ft/lb easier…so we can start with feet (3.14*12 = 37.7) [12 inches in 1 ft]

Here’s the entire formula!
37.7XY*Z = Weight per lineal foot in pounds.

Given specifics…
0.25m-0.82021ft
0.64m-2.099738ft
0.30m-0.984252ft

37.70.820210.099738*0.984252 = 3.035521905941816 ft/lb or 0.925227 m/kg

So 3kg would be 2.775681 meters of pipe.

(Apologies for the math…living in the US I prefer working with Imperial units and converting to Metric system afterward.)

9

Online Version:
http://www.sequoia-brass-copper.com/weight-calc.html

10

I meant chime in…

“Wire puller” is the correct name of what I had in mind.

The density can be given per unit volume, per unit area (section area could be possible in this case) and per unit length, which is what he seems to have.

Julen

11

Here’s a list of helpful formulas for finding specific density/length values I’ve found invaluable in engineering feats :slight_smile: Hope they help!

Rod (Round)
Square of diameter X 9.42 X density of alloy = weight per lineal foot in pounds.

Rod (Hex)
Square of distance across flats X 10.4 X density of alloy = weight per lineal foot.

Rod (Square)
Square of one side X 12 X density of alloy = weight per lineal foot in pounds.

Rod (Rectangle)
Thickness X width X 12 X density of alloy = weight per lineal foot in pounds.

Tube (Round)
37.7 X density of alloy X wall thickness X outside diameter minus wall thickness = weight perlineal foot in pounds.

Tube (Square)
1.27 X the weight of a round tube of the same wall thickness, and of diameter equal to the distance across the flats of the square tube = weight per lineal foot.

Tube (Rectangle)
Width minus wall thickness plus height minus wall thickness X wall thickness X 2 X density of alloy X 12 = weight per lineal foot in pounds.

Pipe
37.7 X density of alloy X wall thickness X outside diameter minus wall thickness = weight perlineal foot in pounds.

Coil Strips
Thickness X width X 12 X density of alloy = weight per lineal foot in pounds.

Circle
Square of diameter X thickness X 0.785 X density of alloy = weight of a circle.

Plate
Thickness X 144 X density of alloy = weight per square foot in pounds.

Sheet
Thickness X 144 X density of alloy = weight per square foot in pounds.

Ring
Outside diameter plus inside diameter X outside diameter minus inside diameter X thickness X 0.785 X density of alloy = weight of ring in pounds.

12

Sorry. This is nonsense in this case, time to go to bed, it’s getting too late here. :slight_smile:

Julen

13

I remember solving a problem like this in calculas class: figuring how a radian measure of a coil of wire relates to it’s length. How the material flexed to different radii when coiled was part of the equation, but it’s been too long I forget what we did.

If the pure math can’t be made accurate enough you can take an empiracal approach. Currently you have some means of measuring your error, that’s how you know your formula is more accurate at the outside and gets worse torwards the center of the coil. So every time you cut off some tube record the winding angles it was cut from and the actual measured weight/length resultant. Plot a few coils worth of data and if it’s accurate enough you should see a trend that shows how length varies with radius. Then match a curve to those points.

14

it took me a while to figure that, but since i have done some plumbery in the past, I know that kind of rolls. I believe the OP’s problem is not how to calculate the length of pipe needed for a given weight. He actually posts that calculus. His problem is because a roll of copper pipe is winded in such a way that each circle in what is in effect a spiral has a different diameter. The smaller inside, the smaller outside. Like on a race track, the inner spirals are shorter. So in effect the innermost spiral is 0.942 meters when the outmost is 2.0096 meters. For those accustomed to US measurements, think in yards (1 yard is 0.9144 meter, close enough for a mental representation).

So as the copper pipe is sold per the circle, the innermost circle weigh only 0.942 * 0.250 = 0.2355 kilogramme (appx half a pound) when the outmost circle weigh 2.0096 m * 0.250 = 0.5024 kg (over a pound). As I posted above Chris did not tell us how many circles (spirals actually) there are in a roll, but it is a pretty simple task to calculate the length of each circle depending on its position relative to the beginning, which seems to be outmost.

Then the problem is to keep a record of the spiral number, to know exactly the length of the next one.

15

So when you refer to pipe, are you referring to a rod (where the is a solid piece of material)? To me a pipe is a cylinder which is long and empty on the inside. The numbers you give for “specific gravity” are in kg/m, whereas these are normally given in the form of a density which is per volume unit and not per length unit. So in your case, the 0.250kg/m comes close to a copper rod (or thick wire) of a gauge somewhere between 2 and 3; whereas a real copper pipe should have a density close 8900kg/m3 (i.e. the density of copper itself). For the later case you take calculate the volume of the outside cylinder (using outside diameter of pipe), the volume of the inside cylinder (using inside diameter of pipe), and the difference of that is the volume occupied by copper itself. That is what you multiply by the density to give you the weight. But your problem doesn’t seem to provide the two diameters of the pipe, and the “specific gravity” is given per length unit, which makes me question what is it you are really referring to.

16

So presuming Michael’s assumption is what the op’s after, then the “specific gravity” provided already took into account the actual amount of copper on each cross-section of the cylinder. So what you are looking for is the equation of a spiral I think.

17

If you go to a hardware store, in the plumbery section, you will see these kind of copper pipe rolls. They are very common. Indeed it is a spiral. Yet it is probably possible to approximate per entire “circle” with a reasonable precision. In this picture there are 12 circles (revolutions), so it is fairly easy to calculate the weight and length per one of them.

18

Isn’t Google useful. http://www.giangrandi.ch/soft/spiral/spiral.shtml.

Of course you may just be better off taking a cut of the profit in the moonshine.

19

Yes they are, but it wasn’t until you made the spiral assumption (at least for me) that the op’s definition of “specific gravity”, (while semantically incorrect), made sense. Again, presuming that is what he is after, the yes it becomes the definition of a spiral. Which is solved by doing an integration of each of the circles. And is approximated by assuming each circle completes each turn and the next circle’s diameter is either the diameter of the previous one minus the diameter of the pipe, or the diameter of the previous one plus the diameter of the pipe (depending on whether you start counting on the inner circle or the outside circle.

20

[quote=167878:@Wayne Golding]Isn’t Google useful. http://www.giangrandi.ch/soft/spiral/spiral.shtml.

Of course you may just be better off taking a cut of the profit in the moonshine.[/quote]

Better calculate before the liquor is tasted :wink:

21

Just curious, why would someone order by weight instead of length? And how do you cut it without unrolling it in the first place?