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I wanted to ask why (how) friction on wet surfaces and friction on dry surfaces have different velocity dependence?

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the classic manner in which friction in the wet state has a different velocity dependence than dry friction is as follows. We use the example of a slab of plywood resting on wet sand.

If you stand on that plywood plank, the water in the sand beneath it oozes out from underneath and the plank is then resting directly on the sharp sand grains, just as if the sand were dry. Lots of friction in this case.

But if you toss the plank so it skims along the surface, it's moving so fast that there is no time available for the water to ooze out from under it. If you now run and jump onto that plank, you will zoom along the wet sand surface with almost no friction because the water presents a film to the plank which prevents the sand grains from rubbing against the bottom of the plank. You are hydrodynamically riding on water, not sand.

In the completely wet case at low velocities- where there's plenty of water always in the way- the laws of fluid dynamics apply, and for velocities that are near-zero, the fluid friction forces tend towards zero. This allows a human with a rope to (slowly) pull a floating barge weighing many tons along a canal.

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