What is the surface height of a still pond after an object is dropped in it?

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SUMMARY

The discussion centers on calculating the surface height of a still pond after an object is dropped into it. Michael seeks a formula that provides a snapshot of the surface height without requiring a time-dependent equation. A recommended resource is the book "Water Waves" by J J Stoker, specifically section 6.6, which discusses the motion of the free surface due to disturbances. The full text is available online, providing valuable formulas and graphs relevant to this topic.

PREREQUISITES
  • Understanding of undergraduate-level mathematics and physics
  • Familiarity with fluid dynamics concepts
  • Knowledge of wave motion in fluids
  • Access to mathematical modeling tools
NEXT STEPS
  • Study the section 6.6 of "Water Waves" by J J Stoker for detailed formulas
  • Research fluid dynamics simulations using software like COMSOL Multiphysics
  • Explore mathematical modeling techniques for wave motion in fluids
  • Learn about the principles of disturbances in still water bodies
USEFUL FOR

This discussion is beneficial for physics students, researchers in fluid dynamics, and anyone interested in modeling the behavior of water surfaces after disturbances.

Michael12345
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I had an idea for a project that would make use of a formula for the surface height of a body of water after an object was dropped in it. I wouldn't need a time-dependent equation, just a nice snapshot...although a general equation (a function of x, y, and t) would be nice. I haven't had much luck finding a solution online, but I'll keep looking. I'm comfortable with undergrad level math and physics, so I don't mind doing some heavy lifting. And if you don't have the time, but can point me to a resource or two, I'd appreciate that, as well.

Thanks,
Michael
 
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An excellent and very thorough book on the subject is "Water Waves" by J J Stoker. And by good luck the full text is available online at www.archive.org. Sect 6.6 is "Discussion of the motion of the free surface due to disturbances initiated when the water is at rest." On or about p 170. Included are formulas, graphs and some photos, although the photos don't show up very well online.
 

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