Formulae re static liquids

[rgdps]

1. I am confused because all my physics was learnt some 40 years ago and I have forgotten how this issue is properly treated . Also all my units tend to lbs, feet, inches etc.....I have not kept up to date with the new units such as newtons etc. Being recently retired, I am trying to build something that requires the facility below:

2. I am inserting a cylindrical cannister through a seal at the bottom of a column of static liquid ( in this instance water). Diameter d inches, length L inches, depth h inches below the surface.

3. I realise that I will expend energy against

3a the force of the pressure (psi)"P" x the cross section area (sq.inches) x length "l" inches.

3b there will be a frictional force "r" based on the cirumference of the cylinder (inches) x the length (inches) x a coeficient of friction for the seal/cylinder contact.

4. The confusion relates to the treatment of the volume of water the inserted cylinder displaces...in that the insertion will cause the level of water in the column to rise and will cause disturbance in the liquid in the column.

The confusion relates to:

4a How would any energy requirement vary in large volume columns as opposed to columns whose volumes closely surround the overall shape and size of the cannister being used?

4b What formula may be used to calculate the effort in this displacement?

4c Is the effort related to pressure ie depth within the column? Or

4d Is it simply the mass of the displacement irrespective of depth?

 

OR

 

4d Does the formula outlined in 3a provide for all this energy required including this displacement as well?

 

Any help you can provide on how this basic physical principle should be considered will be gratefully received.

Thanks Roger.