Abstract
The purpose of this chapter is to develop microscopic balances that are used for the simulation of distributed parameter systems. Distributed systems have spatial gradients as well as time changes. In order to properly describe these systems, the conservation laws must be applied to any point within the system rather than written over the entire macroscopic system. This chapter also be applies these point or microscopic conservation laws to several classical one-dimensional problems that have either analytical solutions or are initial value problems that can be solved using computational techniques. This chapter also introduces simplification of complex problems using order-of-magnitude analysis. It elucidates concepts of conservation of mass and momentum, dispersion, stagnant film diffusion, pipe flow of a Newtonian fluid, and pipeline gas flow.
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