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... let me try to
express it at the 6th grade level for the science teacher that asked me
about it.
To me, scaling laws and conservation laws are the heart and soul
of physics. With a little practice, scaling and symmetry/conservation
arguments become easy to make. They are very powerful. I'm not
saying they solve all the world's problems, but there are quite
a few problems (including the balloon-pop problem) where they
really help. .... The scaling argument gives you an almost-quantitative
picture of what happens ....
Sure, you could write down the fluid equation of
motion in spherical polar coordinates and solve it ... but why
bother? The scaling argument gives you an almost-quantitative
picture of what happens, with incomparably less work.