Free surface of a liquid at rest

[zorro]

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?

 

[kuruman]

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?

 

[zorro]

They wrote 'container of reasonably large size'. I think we have to ignore any boundaries of the container.

 

[kuruman]

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.

 

[olivermsun]

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."

 

[zorro]

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