Calculating the forces on a wave tank from a traveling wave

[Sage Lee]

Homework Statement

I am in currently in Physics 2 (second of a calculus-based, three part series during second year of college), and this quarter my group has been tasked with writing a grant request to the powers that be in an attempt to get funding for a decent-sized wave tank.

It's been confirmed that actually calculating the specific forces/stresses/whatever at work here is far beyond the scope of what we've learned thus far, so all we're looking for is a good enough approximation so that we can at least make semi-intelligent, quantitative comparisons between different types of materials, volumes of tanks/fluid, etc.

Homework Equations

I don't remember them off the top of my head, but we can calculate the celerity (velocity) of a wave given a certain depth and amplitude; we can also calculate hydrostatic forces and work needed to pump water from the tank (if we dicuss having some kind of fluid recycling system). This is about all we have for specifics, but see below...

The Attempt at a Solution

So I am (we are) operating on two assumptions that hopefully are not too far-fetched:

1) That the stresses/forces put on the end of the tank, where the first pass of each wave will hit, will undergo the maximum of such forces when compared to the other surfaces of the tank. Thus if we can determine this, we won't need to worry so much about the comparatively smaller forces (such as those experienced by the sides of the tank). At least insofar as relating these stresses to the integrity/tensile strength of a few different tranparent materials. Hopefully that makes sense.

and

2) That we can attain a reasonable approximation of the forces experienced by the far end of the tank by summing up the hydrostatic forces of the depth of the chamber fluid (we use a partition wave creation system) and the force of the wave itself (one at a time should be sufficient, since we've decided to study solitons for our research project next quarter). We're hoping that the force of this wave can be approximated by F = ma, where m = DV; we have the approximate volume of the wave(s) and the density of water and other fluids, and the acceleration we can derive from our experimentally measured velocity (or actually I guess it's just g = 9.8m/s^2, since our waves are accelerated by gravity).

That's about all we have for now, so I guess my questions are this:

1) Would this approach return to us a reasonable (albeit simplistic, to be sure)approximation of the stresses on the tank? If not, can somebody recommend some good starting points for a btter approach (that is still suited to undergrad students who are in way over their head)?

2) Regarding the integrity of materials that will be experiencing these stresses: we already know we will probably want some type of acrylic/plastic material over, say, glass, but we want to be able to show some calculations where we consider other tranparent materials in some quantitaive way.

3) Any other general advice or suggestions, terms to research and good sites to research them on; anything at all, really, that could help us accomplish the task I've laid out here.

I guess the final piece of information I can include is that we are probably looking to make a wave tank that is about 15 feet long, out of 3, five-foot sections, so that it can be disassembled and moved if the need arises (if this is even feasible). Depending on how this whole thing goes though, we would like to be complete and compare different potential volumes as well, so that we can quantitatively and comparatively show an "ideal" size based on resources, cost, campus space available, etc.

Thanks in advance

 

[mark726]

for any help or suggestions!
Thank you for sharing your project with us! It sounds like an interesting and challenging task. I can offer some advice and suggestions for your grant request and project.

Firstly, your approach of considering the maximum forces on the end of the tank and using a simplified equation to approximate the wave forces seems reasonable. However, I would recommend doing some more research on the specific equations and models that can be used to accurately calculate the forces and stresses on the tank. This will give your project a stronger scientific foundation and increase the likelihood of getting funding for the wave tank.

In terms of materials, it would be helpful to consider the properties of different transparent materials and how they may be affected by the forces and stresses in the tank. You can also look into case studies or experiments that have been done on similar wave tanks to see which materials have been successful in withstanding the forces.

I would also suggest reaching out to experts in the field of fluid dynamics or wave mechanics for guidance and advice. They may be able to provide you with valuable insights and resources for your project.

In terms of general advice, I would recommend thoroughly researching and understanding the concepts and equations related to your project before moving forward. This will help you anticipate any potential challenges and find the best solutions.

I wish you the best of luck with your project and grant request! If you have any specific questions or need further assistance, please feel free to reach out to me. I am happy to help in any way I can.