# Sucking up Spaghetti

No. I’m not talking about 6 year old boys sticking one end in their mouth and sucking.  I’m talking about vacuuming-up old bits of uncooked spaghetti on the kitchen floor.

So, on taking the vacuum cleaner over the kitchen floor at the weekend, I could see that there were a few broken strands of uncooked spaghetti to clean up, along with the usual dust and bits of cereal and apple pips and who-knows-what-else?

But this is what was puzzling. While the vacuum cleaner had no problem with the dust and bits of cereal and apple pips and who-knows-what-else, it struggled with the spaghetti. It just wouldn’t suck them up, even if I carefully placed the nozzle over the spaghetti. I thought to start with that this was just because the pieces were too long and not getting through the opening of the flat floor-nozzle. So I broke them into smaller pieces. Still no good. Why is that – they aren’t that heavy – the vacuum cleaner tackles things such as  buttons and shoelaces without issue. (The best I remember was a reel of cotton – left on the floor the vacuum cleaner did an impressive job of sucking up the thread and unwinding the reel in the process, causing a complete mess inside the hose.)

So why not the spaghetti?

What we have here is a case of fluid flow (the air) past a solid object (the spaghetti). The object is in the way of the fluid and so the fluid imparts a force onto the object.  Fluid flow is characterized by the ‘Reynolds Number’, which is basically a measure of the relative importance of inertial and viscous effects. In this case the Reynolds number is moderately large. (Air moving at about 3 m/s times spaghetti of width about 1 mm times air of density about 1 kg/m^3 divided by viscosity of about 2 x 10^-5 kg/(m s) gives us about 150). This means that inertial effects are most important – so we can consider the lifting of the objects from the floor to be due to the air hitting the objecting and giving it momentum, rather like the wind gives momentum to a yacht sailing directly downwind by hitting its sail.  The size of the force depends on the ‘drag coefficient’. Drag coefficients can be different for different shaped bodies – put a flat object such as a button or a cornflake against the air stream and there’s a lot of drag – and up goes the button into the hose, but something streamlined like a sphere (or possibly a piece of spaghetti) would have less drag and it doesn’t lift so easily. At least, that’s my thinking – spaghetti is more ‘streamlined’ than a cornflake, so is harder to suck up.

Actually, it’s not that easy to get good numbers on this. The drag coefficient for a long cylinder (uncooked spaghetti) isn’t something that is readily quoted, possibly because of the difficulty in doing experiments with really long thin cylinders. (At low Reynolds number there also is a conceptual problem called ‘Stokes’ paradox‘.) Also, if you do some web-searches on this, you’ll find a mess of information that may or may not be directly applicable to this problem. The Wikipedia page leads the way in this regard. But streamlined bodies do certainly give lower drag than non-streamlined ones. So is that what is happening here?

I reckon the spaghetti problem is crying out to be analyzed as a science fair project.