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...Mother Nature has an intrinsic "way" of doings thing "right the first time" after millions of years of evolutionary "trial-n-error," for instance:
"EXAMPLE 10. Blood is transported in the body by means of arteries, veins, artioles, and capillaries. This procedure is ideally carried out in such a way as to minimize the work-energy required to transport the blood from the heart to the organs and back again. Consider the two blood vessels depicted in Figure 9, where r1 > r2." Thus, ie:
cos(phi) = (r2/r1)^(4)
...where:
phi = branch angle between the two vessels
r1 = radius of smaller vessel
r2 = radius of larger vessel
...one of the calculus exercises (page 391) in Grossman's CALCULUS, 2nd ed., 1981, Academic Press.
...she always takes the path of "...least (work energy) resistance..." and it's the same thing with snow and aerodynamics.
P.S.--this equation is VERY handy when you want to merge smaller pipe flow into a larger pipe flow with minimum turbulence and back pressure (ie: header pipes into collectors, etc.).
Last edited by gone-ot; 03-13-2010 at 11:54 AM..
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