Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By hollywood

Math Help - Engineering Optimization Problem (maximum no. of equidistant circles fitting)

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    Manchester
    Posts
    1

    Engineering Optimization Problem (maximum no. of equidistant circles fitting)

    Hi folks,

    I'm an engineer from the UK and I was wondering if any one of you smart lads might be able to help me out with the following problem:
    I'm designing a heat exchanger that needs to fit into a tube of 20in diameter. I would like to have maximum surface area, yet minimal volume in a way, that the heat exchanger tubes (Ds), that are cylindrical, occupy the 20in diameter equidistant from each other (and 0.5 Ds distance from one another), and they cannot be smaller than 1in.
    Any help is appreciated,

    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244

    Re: Engineering Optimization Problem (maximum no. of equidistant circles fitting)

    If you consider the heat exchanger tubes and half the required distance between them as a single object, you are just asking how many circles of diameter 1.25 can be fit in a circle of diameter 20.

    Your question does not have a provable answer. This website:

    The best known packings of equal circles in a circle

    has packings sorted by number of circles, and since your radius is 1.25/20 = 0.625, it looks like the maximum number is 213. It also looks like you might be able to download a file that shows you the pattern for 213.

    - Hollywood
    Thanks from Sajti
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. maximum number of circles in a rectangle?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 5th 2012, 06:37 AM
  2. Replies: 1
    Last Post: February 13th 2011, 07:22 PM
  3. Replies: 8
    Last Post: May 9th 2010, 04:05 AM
  4. Maximum Area (optimization)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 4th 2009, 07:25 PM
  5. Optimization problems(maximum and minim.)
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 1st 2009, 07:02 AM

Search Tags


/mathhelpforum @mathhelpforum