# Fluid Mechanics::'Deriving' Incompressible Flow Criteria

Here we go....

My text attempts to 'derive' an expression that explains when a flow is compressible or not:

Great ... if there's anything I like better than making density approximations, it's playing 'fast and loose' with them.

He then goes on to say:
I am completly baffled as to how we went from (1) to (2) ...let alone from (2) to (3)?
Any thoughts?

Casey

2. Physics news on Phys.org
3. ### tiny-tim

26,055
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)

Also, silly question, but why did we change the ∂'s into $\delta$'s ?