Biomedical Engineering Reference
In-Depth Information
However, the total pressure gradient for a flowing fluid is the sum of the hydrostatic
pressure, the dynamic pressure (related to the fluid velocity), and the pressure associated
with gravity and a height differential. The gravity component is easily described by the
height difference in a fluid manometer. An example of a manometer, which can be used
to measure a pressure difference as a result of the density and gravitational difference
between two fluids, is shown in Figure 14.25.
The total pressure of a flowing fluid is given by
V
2
1
2
P
T
¼
P (hydrostatic
Þþ
r
þ r
gh
Where the hydrostatic pressure is what is normally thought of as “pressure,” the dyna-
mic pressure is given by ½
V
2
, and the last term is the pressure as a result of a height differ-
ential and is measured by a manometer. A pressure transducer can be used to measure the
hydrostatic pressure, a flowmeter is used to measure the fluid velocity (flow rate divided
by vessel cross-sectional area) resulting in the dynamic pressure, and a manometer for the
gravity term. Depending on the density of the fluid and the value for fluid velocity, it is pos-
sible that one of the three pressure components can far outweigh the others. The Bernoulli
equation is a modification of the total pressure equation. It states that the total pressure at
two points is the same or that the sum of the three pressures is equal, as shown following.
r
V
1
2
V
2
2
1
2
1
2
P
1
¼
r
þ r
gh
1
¼
P
2
þ
r
þ r
gh
2
14.2.1 Blood and Fluid Viscosity
Viscosity is a measure of the resistance of a flowing fluid that is being deformed by either
shear stress or normal stress. In general terms, it is the resistance of a liquid to flow or its
“thickness.” Viscosity describes a fluid's internal resistance to flow and may be thought
FIGURE 14.25
Fluid manometer used to measure the density/gravitational pressure difference between two
fluids with varying heights within the manometer. The pressure gradient is a function of the density multiplied
by the height difference in the two fluids.
