9846

Branched Pipe Connection

This Demonstration generates the templates for a branch connection between two cylindrical pipes whose center lines are not necessarily perpendicular and are separated by an offset.
The templates can be used to prepare the metal sheet to weld the two pipes together into a branch connection.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The main cylinder has equation and the branch cylinder has equation , where and are the radii of the two pipes, is the offset between the two center lines, and is the angle between them.
The templates are the unwrapped curves of the intersection of the cylinders [1]. If is eliminated from the equations of the cylinders, a single equation is obtained that can be converted to cylindrical coordinates. This gives the quadratic equation in :
Solving for and squaring the solutions yields the implicit equations for the unwrapped intersection curves:
for the main pipe and for the branch pipe.
Reference
[1] T. M. Apostle and M. A. Montanan. "Unwrapping Curves from Cylinders and Cones." (May 2007) mamikon.com/USArticles/RollingConesCylinders.pdf.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+