Solving Shore Height Difference in "Rendezvous with Rama" (Clarke)

[Redd]

Hi I'm new here and I figured I would post a question that I have thought about but never really understood from "Rendezvous with Rama" (Clarke)


For those of you who aren't familiar in "Rendezvous with Rama" there is a shapeship that is a giant hollow cylinder.
This cylinder rotates to create artificial gravity. okay.

Now the thing I can't figure out:
Rama also has a river that circumscribes the cylinder.
They discover there is a height difference between the two shores of the river. Later a scientist argues that the difference in shore heights is to compensate for when Rama accelerates (meaning it accelerates in the direction of its circular faces). Then the scientist does a few "quick calculations" and determines how much Rama is capable of accelerating.

They know how fast Rama is rotating, Rama's mass and general dimensions as well as the dimensions of the river. I couldn't find the exact dimensions immediatly but I am curious
more for what general method would be best for this problem.

I think my biggest difficulty is that the "force" that is causing the water to slosh back is a pseudo force that is only a result of the water's non-inertial reference frame, and I frankly have always been rather confused by these ideas. Also I haven't studied anything of even basic fluid mechanics so I'm not sure how to treat the movement of the water. I tried doing some weird calculus stuff to determine the amount of work it would require to lift the amount of water, but It didn't lead to anything recognizably fruitfull.

So any insight? Maybe I misunderstood some aspect of the text (anyone particularly familiar?)
Anyway if you have stuck around this long thanks for any responses :)

 

[hamster143]

The tangent of the angle between the surface of the cylinder and the line connecting two shores should be equal to the ratio of maximum acceleration and the centripetal force per unit mass (r*omega^2).

 

[Redd]

The tangent of the angle between the surface of the cylinder and the line connecting two shores should be equal to the ratio of maximum acceleration and the centripetal force per unit mass (r*omega^2).

whoa. That was certainly quick and succinct.

Could you elaborate on this more?

So are you saying the vertical heights ratio to the sideways width is equal to the ratio of the central acceleration to the sideways acceleration?
That seems to make some intuitive sense.
Is it really that direct a relationship?

 

[hamster143]

whoa. That was certainly quick and succinct.

Could you elaborate on this more?

So are you saying the vertical heights ratio to the sideways width is equal to the ratio of the central acceleration to the sideways acceleration?
That seems to make some intuitive sense.
Is it really that direct a relationship?

Yes. Because the combined force should be orthogonal to the surface of the river.

 

[Redd]

Well that was a heck of a lot easier than I was thinking it would be.

Thanks a bunch!

 

[Borek]

It wasn't river, it was Cylindrical Sea.