Mass Continuity Equation Problem

[tophat22]

Homework Statement

Question Details:

The question reads:

Show that the equation:

dA/A + dv/v + dρ/ρ = 0

applies to a one-dimensional steady flow. (Here 'one dimensional' means that both the density ρ and seed v = - v . n (vectors) are constant across any cross-sectional area A cutting the flow.)

Please help!

Homework Equations

d/dt ∫_V ρ dV + ∫_A -ρv⋅n dA = 0

The Attempt at a Solution

I know that the equation they gave us above is the differential equation for ρ*v*A = constant, I just don't know where to go from there.

 

[tiny-tim]

Hi tophat22!

In steady flow, mass in = mass out of any surface, so ρ*v*A = constant.

So differentiate ρ*v*A, and divide by ρ*v*A.

 

[tophat22]

I actually ended up getting it before that... thank you though!