How is Bernoulli's equation related to saxon bowls?

[odysseyinheights]

Homework Statement

This is a lab that we have to design and carry out that goes above and beyond our course. I am investigating how the diameter of a hole in a bowl affects its sink time when put in a larger bowl of water (saxon bowl, or sinking bowl as they are known.) I will have to plot them against each other, yet am not sure how I will do so. This is all I know so far. I need a mathematical model to linearize them once plotted against each other.

Homework Equations

Bernoulli's equation possibly?

The Attempt at a Solution

I think P2 for Bernoulli's equation would be at the hole in the bowl but I am not sure where P1 would be in this case because at the beginning both the water line and the hole in the bowl will be at exactly the same level. I am also not sure how to go from Bernoulli's equation to the diameter and how I would relate them. All I have been able to think of is to calculate the constant for each different hole diameter and compare them? Any help or push towards the right direction, be it an application of the formula or another formula would be appreciated!

 

[Simon Bridge]

It is related to the problem of having a hole in the side of a vessel containing water - but the actual equation is going to be quite complicated.
What you can do is carry out the experiment, then plot the raw data against each other and see what sort of shape you get. Then you can find out what sort of relationship best linearizes the plot that you get.

If the sinking is very slow, you can collect the distance sunk vs time for different hole areas.

For pressures: one pressure is the weight of the top pot pressing down, the other is air pressure at the top surface.
In the initial situation, the pot's weight will displace some water ... you may want to consider plugging the hole and letting the top pot float before unplugging the hole.

 

[256bits]

I think P2 for Bernoulli's equation would be at the hole in the bowl but I am not sure where P1 would be in this case because at the beginning both the water line and the hole in the bowl will be at exactly the same level

Bowl has some buoyancy. The bottom will sink into the water BELOW the water line. You can measure that distance ( with the hole closed so it doesn't start sinking ), or do a calculation if you like, whichever is easier for you. Label the distance from the water line to the bottom of the bowl as "h".

You should now have a P1.

Pretty much what Simon said.