Results 1 to 3 of 3

Math Help - Two-pipe Circumference Problem

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    3

    Two-pipe Circumference Problem

    Please see attached diagram.

    I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

    I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

    I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!
    Attached Thumbnails Attached Thumbnails Two-pipe Circumference Problem-pipes.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    591
    Quote Originally Posted by bbeckett View Post
    Please see attached diagram.

    I have an Engineering problem where straps are to be placed around two pipes. I know the diameter/radius of both pipes and the distance from centre to centre of both pipes. From this information, can I calculate the total strap length (this will be made up of two arc lengths around each pipe and two straight portions tangential to both pipes)?

    I can draw it each time, but it would be useful to have an equation and having failed to work it out myself, I am now intrigued as to whether it can be done!

    I looked at it as a problem of lots of right-angled triangles. I know I need to calculate the angle of the straight portions of the strap, but I lost my way a bit. Does anybody fancy having a go?!
    Take a look here:http://www.mathhelpforum.com/math-he...perimeter.html
    There needs to be a slight adjustment since the circumferences are separated by (C-R-r).

    Let R be the radius of the larger pipe (includes pipe wall)
    Let r be the radius of the smaller pipe.
    Let s be the distance separating the two pipes.
    theta is the angle at the intersection of the tangents to the pipe (theta in radians):

     \theta = 2*arcsin \left( \dfrac{R-r}{R+s+r}\right)

    TotalStrapLength =  R(\pi+\theta) + r(\pi -\theta) + 2\sqrt{ (R+r+s)^2 - (R-r)^2}

    .
    Last edited by aidan; November 18th 2009 at 11:41 PM. Reason: Added equation
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    3
    Thanks very much. It looks so simple now that I can see the answer!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pipe Filling
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 28th 2011, 10:03 AM
  2. Weight of pipe
    Posted in the Algebra Forum
    Replies: 5
    Last Post: February 4th 2011, 09:25 AM
  3. pipe calculations
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 27th 2010, 11:35 PM
  4. Replies: 3
    Last Post: February 15th 2010, 12:53 PM
  5. help with the most economical pipe.....
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 19th 2009, 01:42 AM

Search Tags


/mathhelpforum @mathhelpforum