Finite Control Volume –
Conservation of Linear Momentum
In a Nutshell: For
conservation of linear momentum, the change in linear momentum of the system
must equal the net force on the system.
D/Dt ∫ V ρ dV =
Σ Fsys sys Use
of Reynolds Transport Theorem gives the integral form for conservation of
linear momentum. ∂/∂t ∫ ρ V dV
+ ∫ V ρ V . n dS = Σ
F cv cs
cv = control
volume, cs =
control surface rate
of change of linear momentum in cv + momentum flux
across cs = net force on contents where ρ
is the mass density of the fluid,
Fx and Fy
are forces acting on cv ∂/∂t =
the time rate of change dV =
the element of volume within the control volume V = the absolute 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 Σ F = forces acting on contents within the control volume and on
the control surface Click
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