Tide in an enormous hypothetical canal

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Discussion Overview

The discussion revolves around the hypothetical scenario of a man-made canal spanning one hemisphere at the equator and how tidal forces from the moon would affect the water within it. Participants explore the nature of tidal movement, the formation of waves, and the implications of the canal's design on water behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant proposes that the strength of gravity combined with tidal forces should create a sine wave pattern on the water's surface, but questions how the water would behave in a canal that does not form a complete circle around the Earth.
  • Another participant mentions established methods for calculating tidal movements and suggests that tidal patterns can vary significantly based on location and time of year.
  • A later reply indicates that standing waves would likely form in the canal, with the behavior of the water being influenced by friction, which could cause a phase shift.
  • One participant draws an analogy between nodes and capacitors, and antinodes and inductors, relating tidal forces to alternating current voltage.
  • Another participant expresses a desire for mathematical formulas to address the problem, referencing NOAA resources for tidal formulations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the behavior of the water in the canal, with some suggesting it would form standing waves while others explore different aspects of tidal forces and calculations. Multiple competing views remain regarding the specifics of tidal behavior in this hypothetical scenario.

Contextual Notes

The discussion includes assumptions about the nature of tidal forces and the effects of friction, which are not fully resolved. The complexity of tidal patterns and their dependence on various factors is acknowledged but not exhaustively detailed.

granpa
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imagine a man made canal many km wide and many km deep running the full length of one hemisphere at the equator. let one end of the canal be represented at the origin and the other at x=2π.

the strength of gravity at any point due to the Earth plus tidal forces of the moon should equal a constant plus (I assume) a full sine wave. given enough time the surface of the water should form a sine wave. but as the moon moves across the sky the sine wave representing the force of gravity should move in one direction (at a speed less than the speed of sound in water). if the canal formed a full circle all the way around the Earth then the water would simply follow this sine wave. but because it only stretches across one hemisphere its obvious that the water can't possibly follow the sine wave. so what does the water do. how would I solve this?edit:actually maybe it would just follow the sine wave. the water at each point just moves back and forth so I guess it could.
 
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There are standard ways that have been developed to calculate tidal movement...I tried a GOOGLE on "tidal Forces" and one explanation of many looking conceptually interesting was...

http://csep10.phys.utk.edu/astr161/lect/time/tides.html

Diurnal tides (two highs, two lows daily) here along the east coast of the US occur approximately an hour later each day due to the rotation of the moon. Tides in other parts of the world...and maybe the equator...may follow different patterns. Also the patterns vary by time of year in a given location; Around Jan or Feb in the NY CT area tides are "higher highs" and if they coincide with storms, severe flooding is possible.

I suspect your problem has many answers depending on the accuracy desired...


Also, You may want to check NOAA websites for tidal formulations...
 
after further reading it appears that it would indeed form standing waves after all. if there were no friction each part would try to rise as the moon passed overhead and sink as it moved away. if there were friction it would move out of phase slightly.
 
so I guess, roughly speaking, you could think of the nodes as capacitors and the antinodes as inductors. and tidal forces as an ac voltage.
 
Your post #3 appears practical; I thought you were seeking actual mathematical formulas to solve your puzzle...I have seen tidal formulas over the years, as I noted, I believe NOAA has some posted...
 

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