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Index of Subjects annabelle wrote: > Hi Dave, > It appears that the exponents are screwed up, at least in the message > that came back to us. If it's unreadable or too confusing let me know > and I'll rewrite with a more literal notation. > > Martial Hi Martial & All, Dec 7, 2007 Thanks for the help. The symbol ^ has worked for exponents for me in the past (but retention may depend upon edit settings); some now show in your text within this reply so we will see what happens when sent. I see why cross sectional area will vary with M^(2/3), and if M varies as V^2M^(2/3) then I agree that M will vary with V^6 . But I don't yet see why force varies with V^2 and not V (conservation-of-momentum aspect). Yt, Dave Webster > > annabelle wrote: > >> Hi Dave, >> >> Here’s a back-of-the-envelope dimensional analysis that crudely >> explains why transported particle mass M is proportional to the sixth >> power of fluid velocity V: >> >> The force of the flowing water is reasonably proportional to the >> cross-sectional area of the particle, which is M^2/3. The force is >> also proportional to the square of the velocity (highschool physics >> conservation-of- momentum). So now you have force ~ (V2 ) (M^2/3) . >> >> To transport the particle you reasonably need the force to be of the >> order of magnitude of the mass, i.e. proportional to the mass. So M ~ >> (V2 )( M^2/3), or M ~ V6. >> >> I hope these exponent notations go through ok. >> >> Regards, Martial Thiebaux > >
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