bottle...contd:

I just wanted to add one point: energy is a scalar.
Even a half-full bottle lying on its side with the water in the bottom half, like so:

the above analysis still applies (with the caveat about the actual hydrodynamics), the only difference being that the length of the bottle is replaced with its width.

Moving on, somewhat:

That's the top view of a donut - assumed to be torus, with a circular cross-section, and a circular hole.
Why am I looking at donuts? Because:“Between the optimist and the pessimist, the difference is droll.

The optimist sees the doughnut, the pessimist the hole!” – Oscar Wilde               

Firstly, many doughnuts do not have holes at all. That would imply that pessimists would, perforce, have to eat only doughnuts with holes. Secondly, the sizes of doughnuts – even in the age of cookie-cutter standardization – are not fixed. Nor are their shapes clearly toroidal: or, not clearly having circular cross-sections.

Contrast Wilde’s statement with the more common characterization of the optimist as seeing a glass as half-full, and the pessimist as seeing it as half-empty.

http://www.wou.edu/~burtonl/courses/math494.594/HowDoesYourDoughnutMeasureNoack.pdf

Typical dimensions of a doughnut:

outer diameter: d_o = 9.4 cms

inner diameter: d_i = 2.7 cms

fill factor ff = (d_o)²/[(d_o)² + (d_i)²]

= 0.924

Note: one could calculate a volume ratio, and this would give a different number. The volume of the doughnut is: V = Ac, where A is its cross-section and c is its circumference. The cross-section is:

A = pr², where r = (r_o – r_i)/2 = 4.7 – 1.35 = 3.35 cms.

A = 35.26 cm²

The circumference is: c = 2pR, where R = (r_o + r_i)/2 = (4.7 + 1.35)/2 = 3.025 cms

C = 19.01 cm

V_d = (35.26)(19.01) = 670.29 cm³

Total volume is: V_t = (pR’²)(2r), where R’ = R + r = 3.025 + 3.35 = 6.375 cms

 = 855.43 cm³

Volume fill factor = (V_d)/( V_t) = 0.783

Clearly, Wilde has slanted his definition against a putative pessimist, making his/her job much more difficult. His definition is, of course, the area fill factor and not the volume fill factor.

Not that Wilde was an unabashed optimist: the author of “The Portrait of Dorian Gray” or “Salome” had a clear view of the dark side. It is more likely that he just couldn’t resist the aphorism. 

Of course, the volume fill factor is ambiguous: it could probably be defined differently.

But then, ambiguity was Wilde's forte!