Comparison with the theoretical model

 

 

All that was said and done, while it has its own merit, in order to truly explain the phenomenon we need to verify our model valididty with the designed experiments – respectfully.

The biggest issue was how dependent the model should be to the respective radii of the container (or other geometric values) and the orifice. That particular experiment used containers which were slightly inclined, yet had a flat bottom. This type of container falls under the second of the common cases – the cone.

Additionally, since we cannot measure the height of the cone, that will be determined mathematically, i.e.

 

 

 

 

 

Table 2: Measurements of used container (cups).

 

Hereby, we can use these formulae to predict the rough (average) result and it’s theoretical error:

 

 

 

 

 

 

 

Where  and , i.e.

 

 

 

 

 

We plot the theoretical function for the height (the appropriate container model) as a green continues line. The possible theoretical errors on the model are represented with blue dotted lines. The measured data is represented by red points with red vertical lines representing their error bars.

We can see that the error bars overlap for the first three points (the smallest radii tested). For the following two points they almost overlap. This graph tells us that we’re on the right track.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   Graph 6: Theoretical model vs analyzed data.

 

 

Finally we can see that our model fits the real measurements rather well, some of the points are not in the scope of the prediction, but it could just be the fact that all measurements were made with home tools. Our model lacks a term which is dependent on the shape of the orifice, yet it fares well. This term wasn’t taken into account as we lacked the equipment to even begin to describe such small imperfections. This phenomenon as far as we can tell hasn’t been coined nor investigate under any papers. The project was quite intriguing and rather complicated after we started asking deeper questions. It offered many different perspectives to tackle the problem at hand, some more ideal and simpler, others which lead to on-going research at fluid dynamics.