Page 93 - 4167

which is connected with the dissipation of mechanical energy and its
transformation into a heat. In
the real fluids the internal
friction is the result of

interaction between its particles
(molecules, atoms) and it
characterizes the resistance

which the fluid causes to
change its flow under the
action of external forces. When
at a given study of a fluid
Figure 7.8
internal friction can be
neglected, the fluid is called perfect (ideal) fluid. The simplest example
of the flow of a viscous fluid is the flow between two parallel plates, as

shown in Fig. 7.8. Fluid in contact with each surface has the same speed
as that surface; thus at the top surface the fluid has speedv , while the
2
fluid adjacent to the bottom surface has speed v . The speeds of
1
intermediate layers of fluid increase uniformly from one surface to the

other, as shown by the arrows. In this case the basic (fundamental) law
for the force of internal friction acting in the steady(stationary) laminar
flow of a fluid is established by Newton. The law is:

 v
F   S (7.17)
 z

where: F is the force of internal friction acting between two separate

adjoining layers moving with different velocity (fig.7.8), S -the area of
 v
the frictional surface of the layers, - gradient of velocity (the change
z 
of velocity per of unit distance perpendicularly to the velocity (along the
Oz axis, fig.7.8)).

The coefficient of proportionality  in the Newton's law is called
coefficient of internal friction (dynamical viscosity of the fluid). It is

specific for a given fluid (liquid or gas)and considerably depends on the
pressure and temperature.
The viscosity is equal to the force of friction which acts on one

square meter of two layers of the fluid apart at a distance of 1m when
the difference v between their velocities is of 1m/s. The unit for

92