Environmental Engineering Reference
In-Depth Information
A.4.2
Scale
A dimensionless number can provide an estimate of the relative effect of various
phenomena.
Examples
inertial forces
viscous forces
.
Re
=
A large value of
Re
indicates that inertial forces dominate. Conversely, a small value means
that viscous forces are more important.
kL
D
AB
=
mass transfer resistance in material adjacent to fluid phase
mass transfer resistance in fluid boundary layer
.
Sh
=
A large value of
Sh
indicates that the mass transfer resistance in the fluid boundary layer is
insignificant. A small value means that boundary layer mass transfer resistance dominates.
D
AB
=
fluid kinematic viscosity
solute diffusion coefficient in fluid phase
Sc
=
momentum diffusivity
mass diffusivity
=
.
The relative size of the momentum (M) and concentration (C) boundary layers is given
by:
δ
M
δ
C
=
Sc
n
.
A dimensionless number can also indicate the relative importance of terms in an equation.
See the
Re
example given above.
A.4.3
Solve an equation for a variety of values of the physical quantities
The type of equation and initial or boundary conditions do not change, only their values.
Example
d
C
d
t
=−
kA
V
(
C
−
C
∞
)
.
Initial conditions:
t
=
0;
C
=
C
i
.
This equation describes the concentration change in a batch vessel of volume
V
which con-
tains a sorbent with total surface area
A
. The concentration
C
∞
is that which corresponds
to the maximum loading of the sorbent. Mass transfer to the particle surface controls the
Search WWH ::
Custom Search