Register to reply 
Fluid Mechanics::'Deriving' Incompressible Flow Criteria 
Share this thread: 
#1
Nov1109, 01:44 PM

P: 3,015

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

Sci Advisor
HW Helper
Thanks
P: 26,160

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: 3,015

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

Sci Advisor
HW Helper
PF Gold
P: 12,016

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.



Register to reply 
Related Discussions  
Fluid Mechanics: Inviscid flow v.s. Laminar flow  Engineering, Comp Sci, & Technology Homework  1  
Difference between incompressible viscous and incompressible inviscid flow.  General Physics  1  
Fluid Mechanics: streamlines for a flow  Advanced Physics Homework  0  
Incompressible fluid flow.  Mechanical Engineering  7  
Fluid Mechanics  Pipe Flow  Mechanical Engineering  11 