d_sea_water;grav;meter?decibar
= 1.00518 decibar
I mean why should one ten millionth of the distance from Earth’s equator to its pole have anything to do with the force per area from a column of water under one Earth gravity?
OK… OK… shit happens… I can accept that.
But then answer me this:
Why is it that ten decibars (ie: one bar) is ab/used as an approximation of the pressure of a column of our atmosphere under one Earth gravity?
Am I missing some common definition underlying this?
I don’t understand the Calchemy definition, but in the GNU units program the definitions are as follows (allowing the program to work them out from first principles):
bar = 100000 pascal
pascal = 1 newton/m^2
atmosphere = 1.01325 bar
barye = 1e-06 bar # CGS unit
The Wikipedia page for Pascal (unit) says:
The unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre (N/m2) by the 14th General Conference on Weights and Measures in 1971.
With regard to atmospheric pressure, it says:
The unit of measurement called an atmosphere or a standard atmosphere (atm) is 101325 Pa (101.325 kPa). This value is often used as a reference pressure and specified as such in some national and international standards, such as the International Organization for Standardization’s ISO 2787 (pneumatic tools and compressors), ISO 2533 (aerospace) and ISO 5024 (petroleum). In contrast, International Union of Pure and Applied Chemistry (IUPAC) recommends the use of 100 kPa as a standard pressure when reporting the properties of substances.
It appears to be a coincidence that a unit based upon FORCE/AREA is so close to atmospheric pressure at sea level under standard conditions.
So we have two geocentric coincidences relating to the same physical dimension (pressure). I’m not serious enough about this to immediately take off and write a Mathematica combinatorial script to measure the probability of this. But it is rather a delightful coincidence.
The ‘;’ operator is the lazy man’s way of telling Calchemy to do the combinatorial search for all multiplicative expressions that result in a physical dimension consistent with the unit given after the ‘?’, and then calculate that multiplicative expression’s value with appropriate unit scaling. In the present case, I could have just typed ‘*’ wherever I had typed ‘;’:
d_sea_water;grav;meter?decibar
> d_sea_water * gravity * meter ? deci~bar
= 1.00518 decibar
It also includes a ‘1’ before each of the units if a constant is not given, so a perhaps more understandable “solution by dimensional analysis” would be:
1 d_sea_water * 1 gravity * 1 meter ? 1 deci~bar
which is, of course, equivalent to, but more intuitive than:
1 * d_sea_water * 1 * gravity * 1 * meter ? 1 * deci~bar
The 7 C’s system of measurement
As I’m sure you guessed, his youtube channel is VERY nerdy.
If I didn’t have a million other things to do that is a video I wish I had made.
I’m reminded of perhaps my favorite passage from Stella Maris where Alicia says:
