| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
18 Jan 2007 07:45:26 AM |
| Object: |
Strange shape-what is mathematics behind it? |
Cut the pipe radially at some place so that cut is a perfect circle.
Hold one end motionless. Twist another by 180 degrees. Glue back to the
other end.
Must get a spiral shape .It You turn enough many times, You get double
helix running around in circle. But let us start with 180 degrees. k=1.
What is also of interest, what is the radius of such a shape? How do
You define it?
So where do I have to look for a formula how the radius of such a thing
is defined, and how does it depend on R ( of the initial circle), r (
of pipe) , pi, e, k - number of twists, elasticity of volume,
elasticity of surface?
What is the shape of suface waves?
.
|
|
| User: "Mike Kamermans" |
|
| Title: Re: Strange shape-what is mathematics behind it? |
23 Jan 2007 05:53:55 AM |
|
|
wrote in news:1169127925.984978.109240
@l53g2000cwa.googlegroups.com:
Cut the pipe radially at some place so that cut is a perfect circle.
Hold one end motionless. Twist another by 180 degrees. Glue back to the
other end.
Must get a spiral shape .It You turn enough many times, You get double
helix running around in circle. But let us start with 180 degrees. k=1.
What is also of interest, what is the radius of such a shape? How do
You define it?
The answer to your question relies on first defining what the shape is.
One option is to describe it as a parametric shape, in which case it is
essentially a shape that comes from a creation procedure, like your
textual description of making obtaining the shape in the first place.
Staring from there, we can say "the radius is the same as the radius of
the "pipe", and the closing of the pipe onto itself is a secondary
parameter which we will call a uniform "bend" angle, which in this case
would be 360.
Alternatively, we can look at the shape "as is", rather than as created
shape, in which case the question is not so much "what is its radius",
but more "what is a radius, and does it apply to this shape" - a radius
is the distance of any point on the shape to the center of this shape,
being equal for all points. since this would not be the case with your
shape, the common definition of radius fails, so you're basically free to
define it as you like, provided you keep that definition linked to the
shape. What we can say is that there are three radial quantities we can
define for your shape: the local radial distance from each point on the
shape to the circle that runs through the center of the pipe you used to
make it (which is just the radius of the pipe of course), an inner
spanning radius, which is the inner radius of the pipe as you closed it,
and the outer spanning radius, which is the outer radius of the pipe as
you closed it.
So where do I have to look for a formula how the radius of such a thing
is defined, and how does it depend on R ( of the initial circle), r (
of pipe) , pi, e, k - number of twists, elasticity of volume,
elasticity of surface?
I would be inclined to say "the radius of such a shape is void, it's not
a concept that applies". However, if we go back to the parametric
definition of this shape, then the answers are fairly self evident (but
then we no longer have just one "radius").
Mike Kamermans
.
|
|
|
|
| User: "Jim Black" |
|
| Title: Re: Strange shape-what is mathematics behind it? |
18 Jan 2007 08:01:03 PM |
|
|
wrote:
Cut the pipe radially at some place so that cut is a perfect circle.
Hold one end motionless. Twist another by 180 degrees. Glue back to the
other end.
Must get a spiral shape .It You turn enough many times, You get double
helix running around in circle. But let us start with 180 degrees. k=1.
What is also of interest, what is the radius of such a shape? How do
You define it?
So where do I have to look for a formula how the radius of such a thing
is defined, and how does it depend on R ( of the initial circle), r (
of pipe) , pi, e, k - number of twists, elasticity of volume,
elasticity of surface?
What is the shape of suface waves?
I'm having a hard time following your description. Do you have a
picture you can put on the web and post a link to?
.
|
|
|
| User: "Jim Black" |
|
| Title: Re: Strange shape-what is mathematics behind it? |
18 Jan 2007 08:04:19 PM |
|
|
Jim Black wrote:
ivars.fabriciuss@gmail.com wrote:
Cut the pipe radially at some place so that cut is a perfect circle.
Hold one end motionless. Twist another by 180 degrees. Glue back to the
other end.
Must get a spiral shape .It You turn enough many times, You get double
helix running around in circle. But let us start with 180 degrees. k=1.
What is also of interest, what is the radius of such a shape? How do
You define it?
So where do I have to look for a formula how the radius of such a thing
is defined, and how does it depend on R ( of the initial circle), r (
of pipe) , pi, e, k - number of twists, elasticity of volume,
elasticity of surface?
What is the shape of suface waves?
I'm having a hard time following your description. Do you have a
picture you can put on the web and post a link to?
Never mind, I see it now. Not sure what the answer to your question
is, though.
.
|
|
|
| User: "" |
|
| Title: Re: Strange shape-what is mathematics behind it? |
20 Jan 2007 01:55:32 AM |
|
|
On Jan 19, 4:04 am, "Jim Black" <trams...@yahoo.com> wrote:
Jim Black wrote:
ivars.fabrici...@gmail.com wrote:
Cut the pipe radially at some place so that cut is a perfect circle.
Hold one end motionless. Twist another by 180 degrees. Glue back to the
other end.
Must get a spiral shape .It You turn enough many times, You get double
helix running around in circle. But let us start with 180 degrees. k=1.
What is also of interest, what is the radius of such a shape? How do
You define it?
So where do I have to look for a formula how the radius of such a thing
is defined, and how does it depend on R ( of the initial circle), r (
of pipe) , pi, e, k - number of twists, elasticity of volume,
elasticity of surface?
What is the shape of suface waves?
I'm having a hard time following your description. Do you have a
picture you can put on the web and post a link to?Never mind, I see it now. Not sure what the answer to your question
is, though.- Hide quoted text -- Show quoted text -
These are good references, but so far they fall short of what I was
looking for:
I am looking for a flexible pipe with liquid inside. This pipe then
gets twisted. I doubt that conditions of inextensibility and
unshearability hold in this case. I think criticality parameter formula
may hold in some form, but:
As there is liquid inside, it is possible that at very high viscosity
friction forces can not be neglected.
As the pipe is flexible, most likely even garden hose gets extended
slightly if liquid inside is relatively incompressible.
I am looking forward to more reference suggestions. Someone must have
tackled the problem already, at least formulated it.
I will continue to search among references given, but if someone can
provide a shortcut, I would appreciate that a lot.
.
|
|
|
|
|
|
|
Related Articles |
|
|
