Conservation Laws - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 53

FIGURE 3.3 Atmospheric

Pressure

Schematic of a classic fluid mechan-
ics manometer for measuring the pressure of a fluid
at P . By measuring the differences in height, with a
known open pressure, the hydrostatic pressure at P
can be calculated.

Fluid 1, ρ 1

P

h 2

h 1

Fluid 2, ρ 2

catheter system would not be flowing, but it would maintain the same pressure of the
flowing blood within the vascular system. These systems however are not very accurate
when quantifying pressure because of the effects that they induce on the patient. Most
likely, blood flow within the vessel would be shunted or the vessel would be ligated to
insert the catheter. Therefore, the pressure that is being measured by the manometer sys-
tem is not necessarily the exact physiological pressure, under normal conditions.

Example
Blood is flowing through point P ( Figure 3.4 ), which is connected to a catheter tip manometer
system. Blood enters the manometer and equilibrates the pressure of the various fluids within
the system. Calculate the pressure within the blood vessel.

Solution

p 1 5 p atm 2 ρ 2 g ð z 1 2 z 0 Þ

9 1 mmHg

133

1200 kg
m 3

81 m
s 2

1m
100 cm

p 1 5 : ð Þ :

760 mmHg 2 10 cm 5 751 17 mmHg

: 32 Pa

p 2 5 p 1 2 ρ 1 g ð z 2 2 z 1 Þ

Fluid 1,
ρ 1 = 879 kg/m 3

10 cm

Atmospheric
pressure

1

Blood

P

45 cm

25 cm

2

Fluid 2,
ρ 2 = 1200 kg/m 3

FIGURE 3.4

Schematic of a catheter tip manometer to measure intra-vascular blood pressure.