Fluid Mechanics::'Deriving' Incompressible Flow Criteriaby Saladsamurai Tags: criteria, flow, fluid, incompressible, mechanicsderiving 

#1
Nov1109, 01:44 PM

P: 3,012

Here we go....
My text attempts to 'derive' an expression that explains when a flow is compressible or not: He then goes on to say: Any thoughts? Casey 



#2
Nov1109, 03:47 PM

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Thanks
P: 26,167

Hi Casey!
∂(ρu)/∂x = u∂ρ/∂x + ρ∂u/∂x, so if u∂ρ/∂x << ρ∂u/∂x, we can ignore it, and then ∂(ρu)/∂x ~ ρ∂u/∂x. (2) to (3) is simply rearrangement (and changing u to V for some reason which escapes me) 



#3
Nov1109, 04:07 PM

P: 3,012

Oh...that darned chain rule! Thanks tinytim.
Also, silly question, but why did we change the ∂'s into [itex]\delta[/itex]'s ? Is it because the (∂x)'s 'canceled' and thus it is no longer a derivative, but just a relation between 'changes?' 



#4
Nov1109, 04:09 PM

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Fluid Mechanics::'Deriving' Incompressible Flow Criteria
(2) to (3) is based upon the fact that this argument must be repeated for the v and wcomponents as well, and hence, that the relative infinitesemal change in density must be much less than the relative infinitesemal change in the maximal velocity component, and hence, much less than the relative infinitesemal change in the fluid speed.



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