# Circle vs. Square edge problem

1. Sep 14, 2011

### ISX

I got a problem that I need to figure out. I have a piece of pipe 20 inches long and I bend it on a radius at 90 degrees. I measure from the back of the pipe to the end of one side and get 9, I flip it the other way and do the same thing and get 13.555. If you add those you end up with a right angle vs radius' gain of 2.555 inches. Now the 90* bend is only on part of the pipe as the rest is straight. Is there any way to figure the radius based on just what I said? This isn't homework it's just something I have been working on for a few weeks that is puzzling me like crazy. Thanks.

2. Sep 14, 2011

### gsal

I think I know what you are asking, so, here is something.

First, I am not sure where you are measuring the 9 and 13.555 lengths from/to...it is not clear to me...

But, let's say that you have a 20" long pipe and that when you bend it, the length along the middle of the pipe remains the same.

Then, let's say that you measure the length of the pipe from one end of it to the middle of the 90 degree portion...in other words, you do not measure from one end to the inside of the corner, nor from one end to the outside of the corner...instead, you measure from one end to the middle of the orthogonal 'branch'

Then, I think that having those two lengths, you can calculate the radius to the middle of the corner by:

(x1 - r) + (x2 - r) + 2.pi.r/4 = pipe-length

where x1 and x2 are the two measurements and we take off r to just get the straight portions...then, we add the corner back on (just once)...this should add up to the original length assuming you did not stretch/compress the pipe during bending.

3. Sep 15, 2011

### ISX

I have no idea what orthogonal means. If it means measuring to the start of the bend then that's kinda hard because there is about an inch in a real world scenario where the start of it could be so I can't do that accurately. My measurements were if you bent that pipe at a 90* and had it laying on the ground, but rolled it 90* so that one leg came straight up in the air, you would measure from the ground (back of the pipe) to the end of the leg sticking up. Then you would flip it the other way to measure the other leg.

4. Sep 15, 2011

### gsal

o.k., so you are measuring to the 'back' of the corner...go ahead and take off half the diameter of the pipe from those measurements and apply the equation I have provided.

5. Sep 15, 2011

### ISX

Can you let me know if I did this right.
x1-r+x2-r+(2pir/4)=pl
x1+x2-2r+(6.28r/4)=pl
x1+x2-2r+1.57r=pl
x1+x2-.43r=pl
x1+x2-pl=.43r
(x1+x2-pl)/.43=r

Is that right? I'm not the greatest at algebra.

6. Sep 15, 2011

### gsal

it looks o.k.

just keep in mind that the r calculated this way will also be the radius of the corner but to the middle of the pipe, not to the inside of the corner.

7. Sep 16, 2011

### ISX

Yeah thats really what I needed to find, not the inside or outside radius. Thanks for your help!