Thanks you Andre Assis for a great presentation plus a simpler answer to spinning bucket
Thank you Andre & Spinning Bucket: The Centripetal Answer
I really want to thank Andre Assis for his wonderful presentation this morning. It was an eye opener at least to the idea that Weber conceptualizations concerning electrodynamics should be reconsidered.
And I also fully agree that Weber’s solution may have application to relational mechanics. I actually got up at 4 am this morning to try and read Andre’s book which
I found to be exceptionally well written, relatively easy to understand (even for a simpleton like me). Of course I did not make it to the end but plan to. Moreover I truly thank him for allowing people like me to read it for free. I have my doubts that I could ever be so generous, of giving thousands of hours up for nothing in return. Okay I also live in a completely different world financially speaking but still I fully applaud Andre.
Having said that I remain the simpleton As such a simple sod, the following is my take for the shape of fluid in a spinning bucket. And it is just based upon simpleton logic.
I would like to know if others feel like I do that this or some other simple explanation can explain the bucket and liquid’s shape.
Spinning Bucket: The Centripetal Answer
Take a bucket of spinning water wherein the water moves at the same angular motion as the bucket walls.
From a pressure perspective we can say that the pressure for all molecules along the tensile layer is: Ptensile = 1 atm
This applies to molecules along the tensile layer for booth Fig 1 and Fig 2
Now if the tensile layer is a line of equal pressure, that being 1 atm. Can we not make the realization that the reason that molecule #1 is at a height (h) above molecule #6 (vertex of the parabola) is due to the increase in pressure due to the centripetal forces?
We can expand the above and claim that normally a centripetal force along the x-z plane will cause the force to be only along that x-z plane. If it was not for the bucket’s walls the liquid would spill out radially along the x-z plane (assuming that there were no gravity)
However in the case of the liquid in a bucket the x-z plane is limited by bucket’s dimensions. Therefore the centripetal forces along the x-z planes results in both pressure increase along the x-z plane and an equal pressure increases along the y axis.
The simpleton way of saying this. Pressure is force over area. If we consider a unit of surface area we can say the above is simply due to changes in forces, which is really due to pressure.
Consider molecule 1 which is elevated above molecule 6 by height (h)
Mass/weight of that unit column is: @gh
Where @ is the liquid’s density, g is the gravitational force and h is the height as shown
The force exerted by this unit column should also be: @gh
What is the centripetal force of a unit volume of liquid? Well the unit volume has a mass as defined by the liquid’s density (). It must therefore be: @rww
Sorry for the notation but @rww = @r(w)squared
Equating the forces: @gh=@rww
It is an interesting result as the densities in question drop out. Does this not explain what we see and Andre claims?
Thank you again for reading what I have to say.
-Kent the simpleton