Scaling a Wave Tank: Dimensional Analysis for Design and Construction

[Whatamiat]

I am doing a project to build a scaled wave tank.
"This project involves the design, construction and testing of a wave tank.
When studying the hydrodynamics of a scale model or prototype, it is important to choose an appropriate scale.
To determine tank and wave dimensions it is necessary to carry out dimensional analysis."

Tank will have to mimic
Avg. Wave Height 2.5m
Avg. Wave Period 8secs
Seabed depth of 300m

I have room for up to a 10m long x 1m wide tank.

I will have no problem in designing and constructing the tank once I know relevant dimensions.
My problem lies in the using dimensional analysis to determine the dimensions of the tank and waves.
I have not done D.A before and am lost as to where to even start.

Posted this in homework section but got no reply.
Where do I go from here?

 

[Navin A S]

Dimensional Analysis is a useful tool for scaling the size of models. It involves the use of ratios, known as the Buckingham Pi Theorem. The basic idea is that if you have two sets of variables that are related by a certain equation, then you can use the ratios of those variables to describe how they are related. For example, if you have the equation F = ma where F is force, m is mass, and a is acceleration, then you can use the ratio a/F to describe how the two variables are related. This ratio can then be used to scale the model. To apply this to your wave tank, you will need to find the relationship between the variables in the equation you are using to describe the wave motion. This could be the equation of motion or any other appropriate equation. Then you can use the ratios of these variables to scale the wave tank. For example, if you are using the equation of motion, the ratios of the wave height, wave period, and seabed depth can be used to scale the wave tank. Once you have determined the ratios of the relevant variables, you can then use them to determine the size of the wave tank. For example, if the wave height is 2.5m and the wave period is 8secs, then the ratio of wave height to wave period is 0.3125m/sec. This ratio can then be used to determine the size of the tank. If the tank is 10m long, then the wave height should be 3.125m and the wave period should be 25secs. Once you have the scaled wave tank dimensions, you can then move on to designing and constructing the tank. Good luck!