Teaching by Analogy: The Use of Effort and

Teaching by Analogy: The Use of Effort and Flow Variables
Arthur T. Johnson, University of Maryland, College Park, MD

taught well to students become the foundation for lifelong understanding of physical processes. No set
happens
to the flow once it reaches its destination? It can be stored on capacity, defined as the integ
es is more useful or pervasive than the concepts of effort variables and flow What
variables.
By analogy,
by effort.toThus,
when money crosses the borders of a country, it accumulates and adds to the wealth of a
o almost any situation involving transfer of something from one location or situation
another.

action to occur. They can express the tendency for literal or figurative movement, and are sometimes
al, or field variables. Flow variables are the things that move because of the presence of an effort

uch as fluid flow, heat transfer, and mass transfer conform very well to the effort flow variable concept.
are the effort and flow variables for heat transfer, whereas pressure and fluid flow are the effort and
systems.

ariable analog can extend much farther into such disparate areas as the spread of disease, traffic flow,
psychological motivation and attainment, politics, economics, and even responses to perfume. All of
use and an accompanying flow.

How fast can changes take place? This is limited by inertia,
defined as effort divided by the time derivative of flow. Thus,
despite being highly motivated to begin taking courses (high
effort), and with sufficient cash in hand to pay for them (low
resistance), a student may still take an extra semester to begin
that education because of the need to change habits (inertia).

Relationships between resistance, capacity, and inertia lead to
time constants and natural frequencies that can show how flow
variations can be dampened or magnified. Thus, the more
wealth a nation accumulates, the longer it its economic time
constant, and the less sensitive it is to external fluctuations in
commodity prices.

Teaching students about the principles underlying transport processes, and illuminating the possibilities of
application can enable engineering students to conceptualize in a way that will be forever valuable to them
remain in engineering careers or take other future career pathways. To be agents of change, they will rea
of flow in the presence of a certain amount of effort? The answer is resistance,
defined
effort divided
they
must as
increase
motivation (effort), reduce resistance, overcome inertia, and maintain sufficient capac
ay to contain the spread of disease is to erect barriers (resistance) to its movement,
perhaps through
not be depleted.
sceptible population.

Reference:
Johnson,

A.T. Biological Process Engineering, John Wiley and Sons, 1999.

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