Which Cup Shape is More Prone to Spilling?

[hbj]

If you have 2 coffee cups of equal volume and composition, if one is a shaped like a sector of a cylinder and the other is shaped with a more tapered bowl shape, which is more likely to spill?

 

[Dr. Courtney]

Interesting question. It may depend on what you hold constant: distance from the top edge or volume of liquid in the cup.

 

[hbj]

Interesting question. It may depend on what you hold constant: distance from the top edge or volume of liquid in the cup.

The volume (we had two cups of 8 oz volume and just different shapes).

 

[Drakkith]

If you have 2 coffee cups of equal volume and composition, if one is a shaped like a sector of a cylinder and the other is shaped with a more tapered bowl shape, which is more likely to spill?

Which one do you think and why?

 

[CWatters]

Might be of interest..
http://www.livescience.com/20246-coffee-spill-walking.html

 

[hbj]

My gut tells me that with the cylindrical one there'd be less inertial buildup in the direction of the spill because the forces would be more greatly diffused, but conservation of energy would say that in a round cup eventually those forces have to come around and support the spill. It would just happen later. That would give the spill vector energy time to dissipate.

It sort of "feels" like what's happening when you watch the cups though.

But that's completely a gut feeling of course.

 

[hbj]

Any ideas smart people? :)

 

[Drakkith]

My gut tells me that with the cylindrical one there'd be less inertial buildup in the direction of the spill because the forces would be more greatly diffused, but conservation of energy would say that in a round cup eventually those forces have to come around and support the spill. It would just happen later. That would give the spill vector energy time to dissipate.

Perhaps I misunderstood your question. Are you asking which one will tip over first (and thus spill), or something else?

 

[hbj]

Oh sorry. No I meant given some arbitrary jolt to the cup (with the cup held perfectly parallel to the direction of gravity), which would spill first.

 

[hbj]

Or to put it another way, which would spill with the least energetic jolt?

 

[hbj]

No ideas, eh?

 

[dipole]

You can probably crudely model this using inelastic collisions with some particle of arbitrary or random incidence, and computer on average which shape has a larger upward components of reflection. My guess is the curved cup is worse.

 

[Drakkith]

No ideas, eh?

I'd guess the bowl shape, simply because any liquid trying to flow radially outwards doesn't encounter a wall, but a ramp.

 

[hbj]

Interesting. Thanks!