Skip to main content
Engineering LibreTexts

1.6: Conservation and Accounting - A Useful Framework

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    As discussed earlier, the engineering sciences have traditionally been taught in separate, independent courses. In taking this approach, similarities between the various subjects were often obscured. Because of this students failed to appreciate the significant common threads that run through all of these courses. The goal of this course and the Sophomore Engineering Curriculum is to help you see similarities between the various subjects. It is our belief that in stressing these, we can help you become better problem solvers across a broader range of subjects. In doing this, we believe you will be better engineers.

    So what is the most significant common thread? The answer is the Accounting Principle. A simplified but correct version of the Accounting Principle is presented in Figure \(\PageIndex{1}\). We will refer to this principle throughout the year in the Sophomore Engineering Curriculum. Please note that this principle is not the same as financial accounting; but it is a fundamental concept in physical science. You will find that you already have experience with it and naturally, although subconsciously, use the Accounting Principle daily. For example, when was the last time you balanced your check book?


    Imagine using the accounting principle to reconcile your checkbook with your monthly statement.

    • What should you count?
    • What's the system?
    • What's the time period?
    • Can you produce money? (Legally!)

    Accumulation, or stuff accumulated inside a system in a time period, is the system's input during that period minus the system's output, plus the stuff produced inside the system minus the stuff consumed inside the system.

    Figure \(\PageIndex{1}\): The Accounting Principle

    Application of the Accounting Principle always begins with three questions:

    1. What's the important stuff to count?
    2. What's the system of interest?
    3. What's the time period for counting?

    Why is this single principle so important? Its significance lies in the fact that many of the fundamental laws of physics are based on keeping track of or accounting for extensive properties. When the property counted is mass, charge, linear momentum, angular momentum, energy, or entropy, the accounting principle gives us a common framework to think about and to apply the six fundamental natural laws:

    • Conservation of Mass
    • Conservation of Charge
    • Conservation of Linear Momentum
    • Conservation of Angular Momentum
    • Conservation of Energy
    • Entropy Accounting (The Second Law of Thermodynamics).

    As we will show in the next chapter, conservation is a special case of the accounting principle.

    The coming chapters will demonstrate how the Accounting Principle provides a common framework for engineering problem solving. Chapter 2 will present the basic concepts that underlie the Accounting Principle and its application to engineering systems.

    This page titled 1.6: Conservation and Accounting - A Useful Framework is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Donald E. Richards (Rose-Hulman Scholar) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.