The Physics
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Opus in profectus

Buoyancy

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Buoyant forces act on the foundations of buildings. Tokyo underground train stations need to be pinned down to avoid bobbing to the surface from the buoyant forces caused by increasing water levels.

B = Fbottom − Ftop
B = PbottomA − PtopA
B = (ρfluidghbottom − ρfluidghtop)A
B = ρfluidghA = ρfluidgV = mfluidg
B = Wfluid

Archimedes' principle: The buoyant force (B) on an object immersed in a fluid is equal to the weight of the fluid displaced.

Archimedes of Syracuse (287–212 BCE) was commissioned by King Hiero II of Syracuse to determine if a golden crown made for him was made from pure gold or a low grade alloy as he suspected. The problem was, how to determine the gold content without damaging the crown. As the story goes, Archimedes decided a nice relaxing bath would help him think. He immersed himself in the water and felt a bit lighter — an event experienced by billions of other people on countless occasions. What's unique about Archimedes' relaxing soak was that he realized, for possibly the first time ever in human history, that this buoyant force he was experiencing could be used to determine the quality of the king's crown.

Eureka — perfect indicative form of ευρισκω [eurisko] — to find. Related to the English word heuristics, referring to the methods used to find solutions to problems.

Buoy — "Boiæ genus vinculorum tam ferreæ quam ligneæ." — Festus (Webster's 1913 dictionary). something to do with tying it down with straps? (boiæ?)

The apparent weight (W) of an object immersed in a fluid is given by…

W′ = W − B
W′ = mobjectg − mfluidg
W′ = (ρobjectV − ρfluidV)g
W′ = (ρobject − ρfluid)gV
W′ = ρ′gV

where…

ρ′ = ρobject − ρfluid

is the relative density.

When…

Density of selected materials (~20 °C, 1 atm)
material density (kg/m3)
acetone 790
acid, acetic (CH3COOH) 1,050
acid, hydrochloric (HCl) ????
acid, sulfuric (H2SO4) 1,390
air, 100 K 3.556
air, 200 K 1.746
air, 293 K 1.207
air, 300 K 1.161
air, 500 K 0.696
air, 1,000 K 0.340
alcohol, ethyl (grain) 789.2
alcohol, isopropyl (rubbing) 785.4
alcohol, methyl (wood) 791.3
ammonia 771
aluminum 2,700
argon, gas, ~300 K 1.449
argon, liquid, 87 K 1,430
beer, pilsner, 4 °C 1,008
benzene 870
blood 1,035
body fat 918
bone 1,900
butane 551
butter 911
carbon 2,250
carbon, diamond 3,539
carbon dioxide, gas, +25 °C 1.799
carbon dioxide, solid, −78 °C 1,562
copper 8,960
corn starch, loosely packed 540
corn starch, tightly packed 630
corn syrup 1,380
diesel 800
formaldehyde 1,130
freon 12, liquid 1,311
freon 12, vapor 36.83
gasoline 803
glycerine 1,260
gold 19,300
grain, barley 620
grain, corn, shelled 720
grain, corn, ear 900
grain, flax 770
grain, millet 640
grain, oats 410
grain, rice, rough 580
grain, rice, hulled 750
grain, rye 720
grain, wheat 770
helium, gas, ~300 K 0.164
helium, liquid, 4 K 147
hydrogen (H2), gas, 300 K 0.082
hydrogen (H2), liquid, 17 K 71
honey 1,420
iron 7,870
iridium 22,400
material density (kg/m3)
kerosene 810
lard 919
lead 11,350
lithium 534
lithium 6 deuteride 820
lungs 400
mayonnaise, traditional 910
mayonnaise, light 1,000
methane, gas, +25 °C 0.656
methane, liquid, −90 °C 162
milk, cow, heavy cream 994
milk, cow, light cream 1,012
milk, cow, whole 1,030
milk, cow, skim 1,033
mercury 13,594
monosodium glutamate 1,620
nickel 8,900
nitrogen (N2), gas, ~300 K 1.145
nitrogen (N2), liquid, 74 K 808
oil, vegetable, coconut 924
oil, vegetable, corn 922
oil, vegetable, olive 918
oil, vegetable, palm 915
oil, vegetable, peanut 914
oil, vegetable, soya 927
osmium 22,500
oxygen (O2), gas, ~300 K 1.308
oxygen (O2), liquid, 87 K 1,155
perchlorethylene 1,600
platinum 21,450
plutonium, α 19,860
salt (sodium chloride) 2,165
silicon 2,330
silicon dioxide (quartz) 2,600
silicone 993
silver 10,490
skin 1,050
sodium bicarbonate 2,200
sugar, sucrose 1,550
titanium 4,500
tungsten 19,300
tungsten carbide (WC) 15,630
uranium 19,050
water, liquid, 100 °C 958.40
water, liquid, 50 °C 988.03
water, liquid, 30 °C 995.65
water, liquid, 20 °C 998.21
water, liquid, 10 °C 999.70
water, liquid, 3.984 °C 999.972
water, liquid, 0 °C 999.84
water, ice, 0 °C 916
water, ice, −50 °C 922
water, ice, −100 °C 927
water, sea 1,025
water, saline (0.9 % NaCl) 1,004
zinc 7,140