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Index of Subjects Hi Dave, One factor of V is for momentum and the other is for the rate of transfer of momentum. Think of a cylindrical block of water of length L, density D, and velocity V. Its momentum per unit area is LDV. The time required for the block to move past a fixed point is L/V. Dividing the momentum per unit area by this time gives DV^2. Hence the flux of momentum (or rate at which momentum per unit area passes a fixed point or can be transferred to some object and felt as a force = rate of change of momentum) is DV^2, or proportional to V^2. How are my exponents now? Regards, Martial David & Alison Webster wrote: > > > 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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