Dimensional Analysis The Route to Correlations

The correlations in the previous section provide a useful and compact way of presenting experimental information. Use of these correlations quickly gives reasonable estimates of mass transfer coefficients. However, when we find the correlations inadequate, we will be forced to make our own experiments and develop our own correlations. How can we do this  

We measure the steady-state oxygen concentration as a function of position in the bed. These data can be summarized as a mass transfer coefficient in the following way. From a mass balance, we see that 

Ideally, we would like to measure k and a independently, separating the effects of mass transfer and geometry. This would be difficult here, so we report only the product ka. Our experimental results now consist of the following  

The only way this equation can be dimensionally consistent is if the exponent on time on the left-hand side of the equation equals the sum of the exponents on time on the right-hand side  

Equations 8.4-7 to 8.4-9 give three equations for the five unknown exponents. 

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