When does gravity take over surface tension?

[physnoct]

I want to demonstrate to flat earthers that water does indeed stick to a ball. If we want to do a scale model of the earth, at which radius will gravity overcome the surface tension?

 

[CWatters]

I want to demonstrate to flat earthers...

That would be a waste of time.

 

[CWatters]

Put a drinking straw into a glass of water and the water will rise up the straw until gravity "overcomes" surface tension.

 

[Andy Resnick]

I want to demonstrate to flat earthers that water does indeed stick to a ball. If we want to do a scale model of the earth, at which radius will gravity overcome the surface tension?

The Bond number (Eotvos number) is the ratio of gravitational and interfacial energies: when the Bond number is high, gravity dominates and vice-versa. So all you need to do is write down the Bond number for your scale model and determine what the critical value of 'planetary' mass is (when Bo = 1)

 

[physnoct]

That would be a waste of time.

For FEers, maybe. The question itself is worth an answer, as it is an interesting physics challenge and I would like to know the answer.

 

[physnoct]

The Bond number (Eotvos number) is the ratio of gravitational and interfacial energies: when the Bond number is high, gravity dominates and vice-versa. So all you need to do is write down the Bond number for your scale model and determine what the critical value of 'planetary' mass is (when Bo = 1)

That's a good start! I'll check that. Thanks!

 

[physnoct]

Put a drinking straw into a glass of water and the water will rise up the straw until gravity "overcomes" surface tension.

Is there a formula that I can use?