Measure length without bend ?

Agnishom · 2013-11-20 18:25:27

SuperLynx wrote:

Suppose I have a pipe that is bent to a degree, measuring the length of the pipe from the top to the bottom at 11.76cm. I want to know the length of the pipe as if there was no bend ?

real life situation?

SuperLynx · 2013-11-20 18:25:50

It has an Arc, the pipe is bent.

Agnishom · 2013-11-20 18:54:49

You do not understand my question. Just because something is bent does not mean it is an arc.

Is the pipe a part of a cricle?

Bob · 2013-11-20 19:47:26

I'm going to assume it is part of a circle and try to construct a formula using the various measurements.

This may take a little while ............... thinking ......................................

Bob

Bob · 2013-11-20 21:02:30

hi SuperLynx

See below for my diagram. I have made these assumptions.

The outer arc, AB, is part of a circle.

The inner arc, DE, is part of a smaller circle but with the same centre. (It occurs to me that this may not be true in that the material of the pipe will not allow for two different lengths. You need to decide about this.)

The pipe end, AD (and EB) lies along the radius of the circle (so that AD is perpendicular to the circle at A).

I'm calling the angle ACB, 2 alpha.

I then have a series of formulas. This will give you an idea of how many variables need to be known to solve this problem.

If you know AB, DE and AD then you can work out alpha from equation (2).

Then you can work out R from equation (1).

Then you can work out arc AB from equation (3).

Bob

gAr · 2013-11-20 21:11:18

Hi,

Using formula for arc length of a sector and some trigonometry, we can have the formula:

where s is the pipe length, h is the end-to-end length and θ is the sector angle.
We may verify that s->h when θ->0 and s->∞ as θ->2π.

SuperLynx · 2013-11-21 02:04:16

Is there a simpler method without needing algebraic expressions, I'm sure there is.

Agnishom · 2013-11-21 02:09:01

Yes,.... that method is called geogebra!!

SuperLynx · 2013-11-21 02:22:18

Agnishom wrote:

Yes,.... that method is called geogebra!!

I understand, once again, if I saw a bent pipe.

And I wanted to know it's length before it was bent, since I don't know the history of this pipe can this be found out without algebra ?

gAr · 2013-11-21 02:29:58

What did you mean by 'degree' in the first post?

SuperLynx · 2013-11-21 02:32:43

gAr wrote:

What did you mean by 'degree' in the first post?

Degree as in it's not completely bent, it's bent to a degree, to a angle !

gAr · 2013-11-21 02:49:27

As shown in the figure by bob bundy?

SuperLynx · 2013-11-21 02:54:26

No!

Agnishom · 2013-11-21 03:00:08

I think it is a trick question, the length of the pipe is supposed to be same?! Suppose you have a 100m long rope, it is always 100m long whether bent or not.

I understand, once again, if I saw a bent pipe.

What did you understand? What do you know about geogebra?

I suggest you go to your nearest blacksmith and ask him to unbend it and then measure it.

Bob · 2013-11-21 03:07:16

hi SuperLynx

So what does it look like? Is the picture in post 34 correct?

Bob

SuperLynx · 2013-11-21 03:10:14

The picture in post 34 is not correct, it's close enough.

Agnishom · 2013-11-21 03:13:34

Hi SuperLynx;

Could you please give us some information about where you got the problem or how you got it or why you want it to be done? That might help us understand the problem better

gAr · 2013-11-21 03:26:52

The picture in post 34 is not correct, it's close enough.

Is this figure closer, with negligible pipe thickness?

Bob · 2013-11-21 03:37:10

Agnishom; Yes and replied.

SuperLynx: At the start you asked

Suppose I have a pipe that is bent to a degree, measuring the length of the pipe from the top to the bottom at 11.76cm. I want to know the length of the pipe as if there was no bend ?

That was clearly far too vague because three different responders have each interpreted your problem differently. Would you start again please?

If this is a problem from a book then please give the exact question and diagram.

If this is a practical problem, say how it has arisen and why you need to know.

I cannot guarantee any answer will be simpler; simplicity / complexity depends totally on the nature of the problem itself.

Bob

SuperLynx · 2013-11-21 10:57:36

I don't know what is so difficult to understand. Looking at the pipe image in post #34, you see it's a pipe that is bent. How can you measure it's length as if it was straight, not bent ? I've been told that I need to measure the bent angle of the pipe as well as the other straight areas, is there not a more intelligent way to do this, then having all these measurements at hand ?

bobbym · 2013-11-21 11:30:27

gAr wrote:

As shown in the figure by bob bundy?

SuperLynx wrote:

No!

Then you say

SuperLynx wrote:

The picture in post 34 is not correct, it's close enough.

Okay, you have no drawing that is of the the correct pipe. You have only 1 measurement.

Supposing I pose a counter-question. My kitchen is 8 ft wide. It is rectangular. Of course, I have no drawing or other measurements. How long is it?

SuperLynx · 2013-11-21 11:36:45

Tell me the information you need and why you need it ?

bobbym · 2013-11-21 11:46:37

Since you do not want to use algebra, this is also difficult to understand. Provide a picture of the pipe, and what you call height. With that I will take it over to a CAS and spline fit a curve smack dab through the center of that baby and voila you have the length of the pipe as if it was straightened out.

Of course, we will now have the problem that this will be an approximation. You will need to specify how accurate the approximation should be. 1 digit after the decimal, 2 digits or 100 digits?

Another problem is this method is more complex than algebra and therefore harder to understand and use. This is the price you have to pay for the lack of information.

Last but not least is that something could go wrong and the method fails for known or unknown reasons. Certainly, it is a method no one else will be trying so either I will look like a genius ( more threads about my intelligence can be created, yippee! ) or it will fail miserably and only me and my maker will know how dumb I am. I call that a freeroll!

SuperLynx · 2013-11-21 11:57:32

The picture is in post #34 the measurements are from top to bottom, top of the pipe in the image, to the bottom of the pipe in the image. Those measurements are found in Post #1.

bobbym · 2013-11-21 11:59:13

And the accuracy, in digits after the decimal you require?

Math Is Fun Forum

#26 2013-11-20 18:25:27

Re: Measure length without bend ?

#27 2013-11-20 18:25:50

Re: Measure length without bend ?

#28 2013-11-20 18:54:49

Re: Measure length without bend ?

#29 2013-11-20 19:47:26

Re: Measure length without bend ?

#30 2013-11-20 21:02:30

Re: Measure length without bend ?

#31 2013-11-20 21:11:18

Re: Measure length without bend ?

#32 2013-11-21 02:04:16

Re: Measure length without bend ?

#33 2013-11-21 02:09:01

Re: Measure length without bend ?

#34 2013-11-21 02:22:18

Re: Measure length without bend ?

#35 2013-11-21 02:29:58

Re: Measure length without bend ?

#36 2013-11-21 02:32:43

Re: Measure length without bend ?

#37 2013-11-21 02:49:27

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#38 2013-11-21 02:54:26

Re: Measure length without bend ?

#39 2013-11-21 03:00:08

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#40 2013-11-21 03:07:16

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#41 2013-11-21 03:10:14

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#42 2013-11-21 03:13:34

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#43 2013-11-21 03:26:52

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#44 2013-11-21 03:37:10

Re: Measure length without bend ?

#45 2013-11-21 10:57:36

Re: Measure length without bend ?

#46 2013-11-21 11:30:27

Re: Measure length without bend ?

#47 2013-11-21 11:36:45

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#48 2013-11-21 11:46:37

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#49 2013-11-21 11:57:32

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#50 2013-11-21 11:59:13

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