PHYSICS

to regions of low concentration. All plants utilize water as a solvent;
therefore, osmosis for plant cells means the diffusion of
water through a semi permeable membrane. In order to reach a
state of equilibrium, it is necessary to apply to the solution a
pressure which is equivalent to osmotic pressure of solution. If
water diffuses into the vacuole, its volume will be increased, increasing
the outward pressure on the cell wall. The pressure exerted
on the cell wall which is called turgor pressure (Pr)' At the
same time, the cell wall opposes the pressure of the cytoplasm.
The condition of equilibrium can be written in as:
Pr - P~sm = - P;sm (6.6)
where P~sm and P;sm are the osmotic pressures within and outside
of the cell.
Osmotic pressure plays an important role in phloem transport
in plants and is the driving force in cell elongation during growth.
-­
VI
I
v.....
Fig. 6.4. Flow through
a tube of varying
cross-sectional area
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6.2. FLUID DYNAMICS
6.2.1. The Continuity Equation
This section deals initially with a model of an ideal fluid which
is considered to be non viscous and incompressible. Consider a fluid
flowing through a pi pe of nonuniform size as in fig. 6.4. An incompressible
fluid moving with steady flow through a pipe of varying
cross-sectional area is described by the equation of continuity:
S)' VI = S2' V 2
(6.7)
~
+­
That is, the product of the area
and the fluid speed at all points
along the pipe is a constant. This
equation can be written as:
s = const
V
(6.8)
hI
h 2
6.2.2. Bernoulli's Equation
Consider a situation where the height of the tube above some
reference level also changes (fig. 6.5). Bernoulli's equation states
that the sum of the static pressure (P), the hydrodynamic pressure
pV' (i.e., the kinetic energy per unit volume), and hydrostaticplessure
(pgh) (i.e., the potential energy per unit volume) has
the same value at all points along a streamline:
V
p+p.g.h+~=const, 2
2
(6.9)
where p is the static pressure, p·g·h is the hydrostatic pressure,
and p. v 2 is the dynamic pressure of the fluid.
2 In most problems of biological
interest, h = const, and Bernoulli's
equation becomes:
V 2
p + P ._ = const (6.10)
Fig. 6.5. Flow through a tube of varying
cross-sectional area; the heights of the tube
above some reference level are different
6.2.3. Medical Application of Bernoulli's Equation
Trombosis. The appearance of clots in the blood vessels or the
accumulation of plaque on the inner walls leads to a disease
called trombosis. This situation is accompanied by the constriction
of the vessel (fig. 6.6). If the cross-sectional area of the vessel
decreases, the fluid speed must be increased [see equation (6.8)].
As the speed increases with decreasing area, equations (6.5) and
(6.7) imply that the dynamic
DC]
pressure also increases, but
the static pressure, in order
to maintain a constant flow
Fig. 6.6. Constriction of blood
vessel due to trombosis
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