Friday, July 15, 2022

[hrztynsl] water time

meter and kilogram are elegantly (approximately) linked by the density of water.  calorie and degree Celsius are linked by the specific heat of water.  Celsius absolute values are approximately defined by the freezing and boiling points of water.

(we throw away joule and Kelvin.)

we can define a water-based unit of time by combining these units:

m sqrt(kg / calorie) = 0.48888213 s = 1/176729.72 day

cm sqrt(gram / calorie) = 0.0001545981 s = 1/558868430 day

the conversion factor between SI and cgs is not a power 10 but disgustingly a power of the square root of 10.  (this is worse than the Imperial system.)

standard gravity = 9.80665 m/s^2 = 2.3438456 m/(m sqrt(kg/calorie))^2 = 2.3438456 calorie / m / kg

something similar might be possible with pint or imperial gallon, pound, BTU, and degree Fahrenheit.  pound, BTU, and F are linked by specific heat of water.  but pint (231/8 cubic inch) is not well linked to pound by water density, and imperial gallon, linked to pound by water density, isn't linked to a unit of length.

foot sqrt(lb/btu) = 0.0063198986 s = 1/13671106 day

mile sqrt(lb/btu) = 33.369064 s = 1/2589.2 day

sqrt(acre lb/btu) = 1.3190281 s = 1/65502.8 day

sqrt(acre (US ton)/btu) = 58.988729 s = 1/1464.7 day

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