next message in archive
next message in thread
previous message in archive
previous message in thread
Index of Subjects
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
>
>
next message in archive
next message in thread
previous message in archive
previous message in thread
Index of Subjects