242 Chapter 9 Mass and Mass-Related Parameters
You can express it this way:The rate at which water comes to the tub is equal to the rate at which
the water leaves the tub plus the time rate of accumulation of the mass of water within the tub.
What happens if you were taking a bath and you had the tub filled with water? Let us
say that after you are done taking the bath you open the drain, and the water begins to leave.
Being the impatient person that you are, you slowly turn on the shower as the tub is being
drained. Now you notice that the water level is going down but at a slow rate. The rate the
water is coming into the tub minus the rate at which water is leaving the tub is equal to the rate
of water depletion (reduction) within the tub.
Let us now turn our attention to an engineering presentation of conservation of mass.
In engineering we refer to the tub as a control volume, because we focus our attention on a specific
object occupying a certain volume in space. The control volume could represent the flow bound-
aries in a pump, or a section of a pipe, or the inside volume of a tank, the flow passage in a com-
pressor or water heater or the boundaries of a river. We can use the bathtub example to formulate
a general statement for conservation of mass, which states:The rate at which a fluid enters a con-
trol volume minus the rate at which the fluid leaves the control volume should be equal to the rate of
accumulation or depletion of the mass of fluid within the given control volume. There is also a broad
area in mathematics, operations research, engineering management, and traffic calledqueuing. It
is a study of “queues” of people waiting in service lines, products waiting in assembly lines, cars
waiting in lanes, or digital information waiting to move through computer networks. What hap-
pens during busy hours at banks, gas stations, or supermarket checkout counters? The lines formed
by people or cars grow longer. The flow into a line is not equal to the flow out of the line and thus
the line gets longer. You can think of this in terms of conservation of mass. During busy hours,
the rate at which people enter a line is not equal to the rate at which people leave the line and thus
there is a rate of accumulation at the line. This analogy is meant to make you think about other
issues closely related to the flow of things in everyday life.I think I’ll invite my class here
tomorrow to demonstrate the
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