Object floating on the surface of water

• xyd
In summary, the conversation is about using a function f[x,y,z] to describe the shape of water surface when a tiny object is floating on it based on surface tension. The idea is to balance the pressure and use Laplace's equation and contact angle as boundary conditions. Some references are provided for further exploration.
xyd
How to use a function f[x,y,z] to describe the shape of water surface when a tiny object is floating on it based on surface tension ONLY?

Assume there is a tiny object floating on the water surface because of the surface tension, then the water surface will be deformed obviously. So how can we use a function f[x,y,z] to describe the shape of water surface? (x,y,z) is a set of coordinate system of 3D space.

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AFAIK, this is a solved problem (it's a meniscus) even though I can't find a reference... interesting

The idea is to balance the pressure: the surface will deform in accordance with Laplace's equation ($$\Delta P = -\sigma\kappa$$), and the boundary condition is given by the contact angle. The pressure is given by hydrostatic and contact line forces.

This reference may be a useful starting point:

Or this:

Hey, why no one seems interested in this question?

What causes objects to float on the surface of water?

Objects float on the surface of water because of their density. If the object's density is lower than the density of water, it will float. This is because the upward force of the water, called buoyancy, is greater than the downward force of gravity on the object.

Why do some objects float while others sink?

As mentioned before, the density of an object is the main factor in determining whether it will float or sink. Objects with lower density than water, such as wood or plastic, will float. Objects with higher density, such as rocks or metal, will sink.

Can an object float on water if it is heavier than the water?

Yes, an object can still float on water even if it is heavier than the water. This is because the buoyant force of the water is dependent on the volume of the object, not its weight. So as long as the object's volume is large enough, it can still float even if it is heavy.

What happens to the buoyant force if an object is partially submerged in water?

If an object is partially submerged in water, the buoyant force acting on it will decrease. This is because only the submerged portion of the object is displacing water and creating the upward force, while the rest of the object is not. The buoyant force will be equal to the weight of the water displaced by the submerged portion of the object.

How does the shape of an object affect its ability to float on water?

The shape of an object can affect its buoyancy. Objects with a larger surface area will experience more buoyant force than objects with a smaller surface area. This is because the upward force of the water acts on the entire surface area of the object. Additionally, objects with a concave shape can trap air inside, making them more buoyant.

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