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Name: Dave
Status: Student
Grade: 6-8
Location: N/A
Country: United States
Date: June 2008

I am pouring a cup of milk into a mixing bowl. If I pour the milk quickly, there is no problem, it flows straight into the bowl with either laminar or turbulent flow. However if I pour too slowly, the milk clings to the outer surface of the cup and runs down to the base of the cup, from where it drips onto the floor. My questions are:

1) Am I correct in thinking that this is a demonstration of the Coanda effect?

2)What factors are responsible for the flow switching from laminar flow to adhering to the outer wall of the cup - i.e. is it possible to predict when this effect will occur, and what is the equation that predicts this behaviour? (I am guessing the following may be involved: velocity, density, viscosity and surface tension of fluid, and radius of curvature of the lip of the cup. Are any other factors involved, e.g. temperature of the fluid?)

1. I suppose this could be considered a 'Coanda effect', if you define it broadly enough. Coanda studied air flow, and the Reynolds Numbers for air flow in aircraft are quite different than milk flowing over a cup. So the physics are dramatically different in the two cases. But, if you consider any fluid flowing next to a curved surface as Coanda, then your milk-cup example is in that fold. I would say the novelty of Coanda's discovery had to do with the counter-intuitiveness of the air clinging to a wing, quite different than the milk-cup example.

2. With your milk, you have a surface tension effect (water-type liquids would rather be next to glass than air), and you have an inertia effect (flowing milk, or any mass, will not change direction without having a force applied). If you pour fast enough -- e.g. the milk has enough velocity, its inertia can overcome the surface tension pull. If the flow is too slow, then the surface tension is strong enough to keep the milk attached to the glass.

Turbulent vs. laminar is not the key factor here. This is why I mentioned 'Reynolds Number'. There are two general kinds of flow regimes. First is 'turbulent flow', where fluids spontaneously form eddies and vortices, and second is 'laminar flow' where all the fluid particles are moving in the direction of flow. (These are somewhat 'oversimplified' definitions, but they should be OK for this discussion.) Finding a flow's Reynolds number is the best way to predict if it will be laminar or turbulent. For low Reynolds numbers (low velocity, low density, small size, high viscosity), flow is laminar -- there is not enough energy in the flow for turbulence to develop. For high Reynolds numbers (high velocity, high density, large size, low viscosity), turbulence occurs. Aircraft tend to be high Reynolds numbers, turbulent. Water flowing slowly tends to be low Reynolds number, laminar. The point is this: Fluid can cling to a surface in either flow regime. In the case of Coanda's air, the regime was turbulent. In the case of the milk, the flow is laminar. Both can display the clinging behavior.

Hope this helps,
Burr Zimmerman

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