Finite Control Volume - Conservation of Mass

Key Concept: The Reynolds Transport Theorem provides an expression for conservation

of mass using a finite control volume. The jist of it is that the the mass stored in the control volume plus the net mass flux across the control surface sums to zero.

In a Nutshell: For conservation of mass, the mass of a system must remain constant.

DM_sys/Dt = 0

Click here for a review of the Eulerian method of description. Use of Reynolds Transport

Theorem gives the integral form for mass transfer (conservation of mass).

∂/∂t ∫ ρ dV + ∫ ρ V . n dS = 0 cv = control volume, cs = control surface

cv cs

where ρ = the mass density of the fluid Note: ρ is the intensive property

∂/∂t = the time rate of change

dV = the element of volume within the control volume

V = the fluid velocity crossing the control surface

n = the unit outward normal to the control surface

V . n = the normal component of velocity crossing the control surface (dot product)

dS = the element of area on the control surface

Click here for a discussion on strategy using control volumes.

Click here to continue this discussion.

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