Strategy in the Analysis of Fluid
Mechanics using Control Volumes
In a Nutshell: In the Eulerian point of view, click here for a review if
needed, you observe fluid flow across
portions of a control surface, cs, within which is
the control volume, cv, (a finite volume). Let
b denote an intensive
property. The ones of interest in
fluid mechanics are: mass per unit
mass where b = 1, linear momentum per
unit mass which is fluid velocity, where b = V,
angular momentum per unit mass where b = r
x V, and energy per unit mass, where
b = e. Energy per unit mass, e,
includes contributions from kinetic energy,
V2/2, potential
energy, gz, and internal energy, u . The
strategy described in this section is specific to conservation of mass but
the same basic elements apply to conservation of linear momentum,
conservation of angular momentum, and conservation of energy. For conservation of mass: b = 1,
cv = control volume, cs =
control surface
The
first term above represents the accumulation of the intensive property within
the control volume
and the second term represents the flux of the intensive property across the
control surface. Here b =
the intensive property ρ =
the mass density of the fluid ∂/∂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 table detailing the steps for analysis using control volumes. |
All rights reserved.