[NatureNS] alluvial deposits

Date: Fri, 07 Dec 2007 09:35:47 -0400
From: annabelle <hamst@xplornet.com>
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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


David & Alison Webster wrote:
> Dear All, Dec 6, 2007
> I see in my old Forest Soils text that the size (weight) of particles 
> that can be transported by flowing water varies as the sixth power of 
> the velocity, i.e. if particles of size X can be transported at 
> velocity v then at 2v particles of size 64X can be transported.
>
> Can anyone take a stab at explaining the physics of a dX/dv this large ?
>
> Yt, Dave Webster, Kentville
>

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