WOLFRAM|DEMONSTRATIONS PROJECT

Compression Ratio of Spheres in a Curved Tube

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bend radius to sphere radius b/s
5
tube radius to sphere radius t/s
1
sphere opacity
0.5
wall opacity
0.5
This Demonstration determines the optimal packing for spheres in a curved tube. Spheres of radius
s
are packed in a tube of radius
t
, where
t≥s
, with a
°
180
bend of radius
b
. We seek the minimum value of the compression ratio. For small ratios
t/s
, the spheres are in contact with the outside wall. For larger
t/s
, optimal compression is attained by arranging the spheres in a zigzag pattern parallel to the axis of curvature along the tube centerline.