[NatureNS] alluvial deposits

Date: Fri, 07 Dec 2007 20:55:54 -0400
From: annabelle <hamst@xplornet.com>
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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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