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

• Nov 25th 2012, 03:08 PM
Sajti
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
• Nov 25th 2012, 08:17 PM
hollywood
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.