Engr Help

Finite Control Volume – Conservation of Mass and Linear Momentum (Deformable CV)

Key Concept: Conservation of mass and conservation of linear momentum with a deformable

control volume must include the term involving rate of change of mass or of linear momentum

within the control volume.

In a Nut Shell: The strategy for both conservation of mass and for conservation of linear momentum

is to apply the complete equations

For conservation of mass: ∂/∂t ∫ ρ dV + ∫ ρ V . n dS = 0

cv cs

For conservation of linear momentum:

∂/∂t ∫ ρ V dV + ∫ V ρ V . n dS = Σ F acting on contents of the control volume

cv cs

where the terms involving the control volume are no longer zero.

The term ∂/∂t ∫ ρ dV represents the change of mass within the control volume.

Note, the mass within the control volume could be increasing or decreasing with time.

The term ∂/∂t ∫ ρ V dV represents the change of linear momentum within the control volume.

Again, it could be increasing or decreasing with time.