Conservation Laws - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 52

Notice that in the above example, the absolute change in pressure remains the same at
the end of systole and diastole (

Δ p

23.18 mmHg). This change in pressure is constant
because we assumed that the height and the blood density did not change. Again, this is
only valid if the three assumptions we made to derive this formula can be applied to the
particular example.
The previous example brings us to an important distinction in fluid statics situations.
All pressures must be referenced to a specific reference value. For instance, we may have
chosen to call the pressure at the aortic valve 0 mmHg, and this choice would make the
cranium pressure exactly

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23.18 mmHg for each of the two cases in the previous example.
This is true even when the aortic pressure is variable, because it is our reference and is
defined as 0 mmHg at all times. There are two types of pressures that we can discuss. The
first is the absolute pressure, and the second is the gauge pressure. Absolute pressure is in
reference to a vacuum; this would also be the absolute (or exact) pressure of the system at
your particular point of interest. Gauge pressure is the pressure of the system related to
some other reference pressure, which is conventionally atmospheric pressure. Therefore,
gauge pressure is actually a pressure difference and is not the actual pressure of the sys-
tem. In our example above, 120 mmHg and 80 mmHg are gauge pressures. This means
that the actual pressure at the aortic valve would be 120 mmHg plus 1 atm (which would
be equal to an absolute pressure of 880 mmHg). In this textbook, we will refer all gauge
pressures to atmospheric pressure, so that
p gauge

2

p absolute 2 p atmospheric

5

Equation 3.10 describes the pressure variation in any static fluid. Changes in the pres-
sure force are only a function of density, gravity, and the height location, assuming that
the gravitational force acts only in the z-direction. In the previous example, we made the
unstated assumption that changes in gravity are negligible. For most practical biofluid
mechanics problems, the variation in the gravitation force with height is insignificant.
Assuming that gravity is 9.81 m/s 2 at sea level, for every kilometer above sea level gravity
reduces by approximately 0.002 m/s 2 . Therefore, when the height changes that are being
described are on the order of meters or centimeters (which will be typical in this textbook),
the change in gravity with height can be neglected. This is a reasonable assumption.
However, in some biofluid situations, it may not be a good assumption that the density is
constant, so be careful applying this rule.
Remember our definition for incompressible fluids; the fluid density is constant under
all conditions. In this situation, it would be appropriate to use Equation 3.10 , in the form
shown in the example problem. The pressure variation in a static incompressible fluid
would then be

p p 0 2 ρ g z ð z z 0 Þ ð 3 : 11 Þ

5 2

A useful instrument to measure pressure variations solely based on height differences
is a manometer. In classical fluid mechanics examples, manometers are used extensively
to determine the pressure of a fluid compared to atmospheric pressure ( Figure 3.3 ).
Relating this to a biological example, manometers have been coupled to catheter systems
in order to measure the intra-vascular pressure relative to atmospheric pressures. Even
though the blood is flowing within the blood vessel, the blood that was diverted into the