Advanced Engineering Mathematics, 7th Edition

8.17 Discrete Compartmental Models

INTRODUCTION

The construction of the mathematical model (3) in Section 2.9, describing the number of pounds of salt in two connected tanks in which brine is flowing into and out of the tanks, is an example of compartmental analysis. In the discussion in Section 2.9, the compartmental model was a system of differential equations. In this section we introduce the notion of a discrete mathematical model.

The General Two-Compartment Model

Suppose material flows between two tanks with volumes V₁ and V₂. In the diagram shown in FIGURE 8.17.1, F₀₁, F₁₂, F₂₁, F₁₀, and F₂₀ denote flow rates. Note that the double-subscripted ...