7.8. DIMENSIONAL ANALYSIS IN MASS TRANSFER
7.8A. Introduction
The use of dimensional analysis enables us to predict the various dimensional groups which are very helpful in correlating experimental mass-transfer data. As we saw for fluid flow and heat transfer, the Reynolds number, Prandtl number, Grashof number, and Nusselt number are often used in correlating experimental data. The Buckingham theorem discussed in Sections 3.11 and 4.14 states that the functional relationship among q quantities or variables whose units may be given in terms of u fundamental units or dimensions may be written as (q − u) dimensionless groups.
7.8B. Dimensional Analysis for Convective Mass Transfer
We consider a case of convective mass transfer where a fluid is flowing by forced convection in a pipe and mass transfer is occurring from the wall to the fluid. The fluid flows at a velocity ν inside a pipe of diameter D, and we wish to relate the mass-transfer coefficient 
to the variables D, ρ, μ, ν, and DAB. The total number of variables is q = 6. The fundamental units or dimensions are u = 3 and are mass M, length L, and time t. The units of the variables are
The number of dimensionless groups of π's are then 6 − 3, or 3. Then,
Equation 7.8-1
We choose the variables DAB, ρ, and D to be the variables common to all the dimensionless groups, which are
Equation 7.8-2
Equation 7.8-3
Equation 7.8-4
For π1 we substitute the actual dimensions as follows:
Equation 7.8-5
Summing for each exponent,
Equation 7.8-6
Solving these equation simultaneously, a = −1, b = 0, c = 1. Substituting these values into Eq. (7.8-2),
Equation 7.8-7
Repeating for π2 and π3,
Equation 7.8-8
Equation 7.8-9
If we divide π2 by π3 we obtain the Reynolds number:
Equation 7.8-10
Hence, substituting into Eq. (7.8-1),
Equation 7.8-11
