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Problem 45396. Design a tubesheet for shell-and-tube heat exchangers

A tubesheet is a metal plate used to hold multiple tubes in place in a shell-and-tube heat exchanger. In any industrial plant, heat exchangers are used to transfer heat from one stream to another, such as for cooling or heating.

In this problem, you are given the diameter D of a metal plate which is a perfect circle. We need to punch holes in this plate where the tubes can fit in. This is done by placing the plate on a 2-D coordinate system where the center of the circle lies in the origin. As seen in the figure below, the coordinate system can be imagined as being made of square cells. A hole can be punched in a square cell if and only if it lies completely inside the circular metal plate. Can you help count the number of holes we can punch, given the plate's diameter?

Access the figure here: https://drive.google.com/open?id=16fQsnGyJz-PQLF9Hw7koIKKscPu6whFM

Write a function that accepts a floating-point value, D. Output the maximum number of holes that can be punched on a plate of diameter D. You are ensured that 1 <= D <= 50.

In the examples above, we can see that we can punch 16 holes when D = 6, and 60 holes when D = 10.

Solution Stats

18.97% Correct | 81.03% Incorrect
Last Solution submitted on Jun 12, 2020

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