Finite Control Volume –
Conservation of Mass and Linear Momentum
(translating CV)
In a Nut Shell: The strategy for both conservation of mass
and for conservation of linear momentum is
to replace the absolute fluid velocity, V,
with the velocity of the fluid relative to the translating control
volume, W. The
figure below shows the vector representation of the absolute fluid velocity, V, the absolute velocity
of the control volume, Vcv, and
the velocity of the fluid with respect to the translating control
volume, W. In
steady flow (no change with time),
the equation for conservation of mass with
a translating
control volume moving in a straight line at a constant speed is: ∫ ρ W . n dS = 0 cs In
steady flow (no change with time),
the equation for conservation of
linear momentum with
a translating control volume moving in a straight line at a constant speed
is: ∫ W ρ (W . n ) dS =
Σ F cs where ρ is the mass density of the
fluid, n is the unit outer normal to the control surface, dS is the
element of area on the control surface,
and Σ
F
is the sum of all forces acting within the control
volume and on the control surface |
Copyright © 2019 Richard C. Coddington
All rights reserved.