Inspired by a textbook on blood vessels that used bike tyres vs car tyres to try and explain why bigger blood vessels need thicker walls than thin blood vessels, even with the same internal pressure.

So – if you have a thin tube – say 1 cm circumference – and a much wider tube, say 10 cm circumference – how does the wall thickness need to change to support the same internal pressure, assuming it’s the same material?

10x (off the top of my head)

Ah! Laplace.

http://hyperphysics.phy-astr.gsu.edu/hbase/ptens.html#lap2

Diagram at the bottom with the cable works for my brain.

Ah! Laplace.

Runs off screaming. Aaagghhh.

Just about managed to explain it to MsBeej with a headphone cable and some scissors hanging from it. She’s doing a clinical diploma and is doing cardiovascular stuff.

hoop stress = pr/t

to keep the stress approximately the same the wall thickness must increase proportionally

Simple way to think of it is to consider the tube sliced in half horizontally on the diameter. The pressure in the fluid across the cut is then resisted by the tension in the walls at the point of the cut. So the load in the wall is always pressure times half the diameter (all per unit length of pipe). 10x the size, 10x the load in the wall.