Dimensionless numbers - Principles of Chemical Separations with Environmental Applications - page 276

number). It is equivalent to use either since we would still have three s. We have not

violated any constraints with this rearrangement. We have simply multiplied both sides of
our original functional form ( kL

)by Sc .
This illustrates an important point. With this method, we can obtain dimensionless
numbers but they may not be in the best (or most recognizable) form. So the final form
that is normally used is:

/ν

Sh = f ( Re , Sc ) .

These dimensionless numbers have physical significance which is usually more useful
than the original set when correlating data.
Correlations for mass transfer coefficients in this and other texts will have this functional
form for similar flow situations.

A.3 Putting an equation in dimensionless form

Consider flow across a horizontal flat plate.

0.99 of C = typical

definition of value
corresponding to top
of concentration
boundary layer
d = concentration boundary-layer
thickness
(usually not the same value as
momentum boundary-layer
thickness)

∞

u , C

∞ ∞

y

x

L

u : velocity in x -direction
v : velocity in y -direction

Steady-state convective diffusion equation ( x -direction) after simplification:

u ∂

2 C A
∂

C A
∂ x + v ∂

C A
∂

D AB ∂ = .

y y 2

Each variable needs to be incorporated into a dimensionless form.
Each constant (i.e., D AB ) is left “as is.”