PROBLEM SET 5.3: HEMODYNAMICS AND MICROCIRCULATION
ANSWER KEY
1. A normal individual experiences a deep cut that severs the radial artery near the
... [Show More] elbow. Ignoring air
resistance, approximately how high will the blood spurt? (Hints: the specific gravity of blood is 1.050
g cm-3 and the specific gravity of mercury is 13.6 g cm-3 )
Strictly speaking, the only determinant of the height of a column of blood is the velocity at which it
exits the artery. This depends somewhat on the size of the hole cut into the artery. We can estimate
this height by noting that a column of blood at equilibrium with the blood pressure will reach a height
at which the pressure of the column of blood is equal to the blood pressure. This is the case when
all of the pressure energy and kinetic energy is converted to gravitational potential energy. From Eq.
(5.8.5) we have
P’ = P + ½ D v2
+ D g h
where P’ is the net equivalent pressure, P is the hydrostatic pressure, ½ D v2
is the kinetic energy and
D g h is the gravitational potential energy. At the top of the column of squirting blood, P goes to zero
and ½ D v2
also goes to zero. Thus all of the pressure is converted into a column of fluid h units high.
The pressure of a column of fluid is
m g / area
where m is the mass, g is the acceleration due to gravity and area is the area of the column of fluid.
The mass of the column is given as m = v x D where v is the volume and D is the density. For a right
cylinder, v = area x h where h is the height of the column. Thus we have an equation
Area x hblood x 1.05 g cm-3 /Area = Area x hHg x 13.7 g cm-3 /Area
or
hblood = hHg x 13.7/1.05
If the systolic pressure is 120 mm Hg, the blood should rise to a maximum height of
hblood = 12 cm x 13.7/1.05 = 156.6 cm
This is 61.65 inches, or a little more than 5 feet. This is just enough to reach the ceiling in most
houses (8 feet) if you are lying on a table 30" off the floor and you allow 6" between the table and the
point of incision.
The reality is that the blood will not go that high, because the flowing blood already converts some
of its pressure energy to kinetic energy of the blood and dissipates some of it by friction. [Show Less]