Free surface of a liquid at rest

In summary, the free surface of a liquid at rest in a reasonably large container is always horizontal due to the absence of relative acceleration between the liquid and the container. If there is a relative velocity between the two, the free surface may not be horizontal. However, the exact behavior depends on the specific boundaries of the container and the properties of the liquid.
  • #1
zorro
1,384
0

Homework Statement



The free surface of a liquid at rest contained in a container of reasonably large size is always seen to be horizontal. Can we say that it is a consequence of
i) the absence of relative velocity between the liquid and the container
ii) the absence of relative acceleration between the liquid and the container ?

The Attempt at a Solution



i) If we assume the relative velocity to be constant, then the free surface would be horizontal. So we cannot ascertain the condition given.

ii) There would be a pseudo force on the water in the container giving it a slanted free surface if there is a relative acceleration b/w the two. So its absence is responsible for horizontal free surface.

Are my answers and reasoning correct?
 
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  • #2
Regarding question (i): What do you think would happen if the relative velocity between a liquid and its container is constant? To be specific, if you have water in a glass and the water is moving at constant 50 km/hr while the the glass is moving at constant 30 km/hr, what would happen? :rolleyes:
 
  • #3
They wrote 'container of reasonably large size'. I think we have to ignore any boundaries of the container.
 
  • #4
Abdul Quadeer said:
They wrote 'container of reasonably large size'. I think we have to ignore any boundaries of the container.
That's what I find troubling with "them" who wrote the question. It is not clear how "they" expect you to model the fluid. On one hand, if you completely ignore the boundaries of the container, then you don't have a "contained" fluid. In that case the container can do what it wants (dynamically) and that would be independent of what the fluid does. On the other hand, if you ignore some of the boundaries but not others, which ones do you ignore and which ones do you keep?

I know I am not really helping you here. Maybe someone with better insight than me can pitch in.
 
  • #5
I believe that the "reasonably large size" is a nod to a common observation in small laboratory containers, which is that the surface tension of the water causes a noticeable curvature. Ignoring that effect, the surface of the liquid is indeed horizontal, even if the container is "tilted" relative to horizontal.

To go back to the earlier post by kuruman, I would ask how the two possibilities (i)-(ii) mesh with the statement that the liquid is "at rest."
 
  • #6
olivermsun said:
To go back to the earlier post by kuruman, I would ask how the two possibilities (i)-(ii) mesh with the statement that the liquid is "at rest."

May be the liquid is rest with respect to the liquid :biggrin:
 

1. What is the free surface of a liquid at rest?

The free surface of a liquid at rest is the surface of the liquid that is not in contact with any other material or solid surface. It is the topmost layer of the liquid that is exposed to the air or any other gas above it.

2. What causes the free surface of a liquid to form?

The free surface of a liquid is formed due to the cohesive forces between the liquid molecules. These forces cause the molecules to stick together and form a surface tension, which creates the free surface.

3. How does gravity affect the free surface of a liquid at rest?

Gravity is the main force that determines the shape and height of the free surface of a liquid at rest. It causes the liquid molecules to pull down towards the center of the Earth, creating a flat and level surface.

4. Can the free surface of a liquid at rest change in shape or size?

Yes, the free surface of a liquid can change in shape or size depending on the conditions it is in. This can be influenced by factors such as temperature, pressure, and the presence of other substances in the liquid.

5. What is the significance of the free surface of a liquid at rest in scientific research?

The free surface of a liquid at rest is an important aspect in many scientific studies, such as fluid mechanics, hydrodynamics, and surface tension. It helps researchers understand the behavior and properties of liquids, and how they interact with their surroundings.

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