Fundamentals of Fluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 16

of interest would be the blood vessel and everything within it, and the boundaries of our
system of interest would be the vessel wall. These boundaries are movable with time, but
mass cannot cross this boundary (at least within the macrocirculation). This is the key to
defining the system properly. For instance, if your system is an un-inflated balloon, then
no mass (e.g., helium gas) can cross into this boundary; hence, the balloon would remain
un-inflated ( Figure 2.9 A). However, if you choose your system to be the balloon plus the
nearby helium tank, the balloon can be inflated during the course of the example
( Figure 2.9 B). In this same situation, the system boundary will also be variable with time.
When the valve to the helium tank is closed (time zero) the system boundary is the flat-
tened un-inflated wall of the balloon. However, as you open the tank valve, the balloon
gains mass and volume and the system boundary will follow the balloon wall. The same
is true for biofluid problems that include the lungs; it is wise to include the atmosphere in
the system of interest, if the problem deals with inspiration and exhalation.
As stated previously, a free-body approach is used extensively in mechanics of solids.
This is an easy approach because a system can be chosen with a defined mass and this
mass will generally not change with time (for general solid mechanics problems).
However, in fluid mechanics, the flow of fluids through a device (pipe, turbine, blood ves-
sel) is the most interesting problem. Therefore, it is not easy to define a finite mass that we

FIGURE 2.8

Two common ways
to set up the coordinate axes in a
solid mechanics problem. Either
convention can produce a solution
but the solution using the coordinate
axis shown on the left would gener-
ally work out easier than the right
coordinate axis because many vari-
ables are aligned with that axis
system.

Y Y

X

X

A B

FIGURE 2.9 Two

choices for the system of
interest (dashed line).
With the first choice (A)
the balloon will remain
uninflated for the entire
problem because no mass
can transfer through the
system boundary. For the
second choice (B) the bal-
loon can be inflated and
the boundary would fol-
low the balloons wall in
time.

He He