# Water (F 1 ) is blended with a stream F 2 with 40% ethanol to make a

## Question:

Water (F_{1}) is blended with a stream F_{2} with 40% ethanol to make a whiskey product that is 30% ethanol. Assume F_{1} = 4 gal/min and F_{2} = 4 gal/min.

(a) Develop a steady-state material balance model for the blending operation. Find the linearized gains for the 2 × 2 transfer function model using Example 18.3 as a guide. F_{1} and F_{2} are manipulated variables, and the controlled variables are the outlet composition z and the total ﬂow rate F.

(b) Derive the RGA in terms of F_{1}, F_{2}, and F.

(c) Determine the RGA and the preferred pairing for the controllers.

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**Related Book For**

## Process Dynamics and Control

**ISBN:** 978-1119385561

4th edition

**Authors:** Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp, Francis J. Doyle