Two pipes are bound tightly togehter with a very thhin wire. the radii of the pipes are 2 inches and 6 inches.

Question

...Neglecting any practical allowances for securing the wire, etc. Determine the minimum length of the wire. Please explain. Thanks!

Answer 1

Okay, first the angle of the line tangent to both pipes needs to be found, which is:

Arcsin((6-2)/(6+2))

From this, we can deterimine the length of the wire in contact with each of the pipes as follows:

2(π - 2Arcsin((6-2)/(6+2)))

6(π + 2Arcsin((6-2)/(6+2)))

Add to this the length of wire between both pipes:

2√((6+2)²-(6-2)²)

The sum of all this comes to

(4/3)(6√3 + 7π)

or approximately 43.1779

You may need to draw out a picture to follow this.

Answer 2

About 41 inches?

I have no real formula for it, just did it in my head.

The length of the two pipes together is 16 inches as determined by adding the diameters. So you have the wire going across the side of the two pipes.

The turn around one pipe *might* be determined by measuring half of the circumference...this is what I'm not sure about, but it's ~6.28 inches for the smaller pipe.

Then you have to go back down the length of the pipes, so add another 16 inches from the sum of the diameters.

Now around the bigger pipe, half of the circumference is ~18.84 inches. Again, I'm not sure about this step.

Add them all together to get the total length, which is ~57.12 inches. I'm no master mathematician or anything so if you're doing this for school just consider it a suggestion.

EDIT: Actually, I think it may be ~41.12 inches. If you're going to use half of the circumference to measure that curve, you have to start halfway across the pipes. So subtract half of the diameter on each end.