Episode 17: Nuclear reactor modelling

This week the topic was mathematical modelling and linear programming. We interviewed Rick Crawford from AMEC, who’s a mathematician studying decommissioning of nuclear reactors, and using mathematical models to determine whether it’s safe to continue using a particular reactor given that it may have degraded over time, but without actually building a physical model of it.

Interesting links:

• Nuclear Power Plant at HowStuffWorks
• Mathematical model on Wikipedia
• Small angle approximation at John Cook's blog The Endeavour
• Linear programming at Purple Math

Puzzle: A rod sits inside a cylindrical tube of the same height. The tube is 193mm tall, and 50mm in diameter. We assume the rod has zero thickness. What’s the maximum angle away from vertical that the rod can make (to the nearest degree)?

Solution:

You can imagine the rod as being a line inside a rectangle, since the cylinder is the same all the way round. Then, you need to calculate the angle made by the rod when it’s touching one bottom corner of the rectangle and resting against the opposite side. This will be a triangle whose base is 50mm and hypotenuse is the length of the rod. The angle from the vertical will be the top corner, and the sin of this angle will be the opposite (base of the triangle) over the hypotenuse. So the angle will be sin(50mm/193mm), which is 15 degrees to the nearest degree.