DOC.
4
KINETIC
THEORY
LECTURE NOTES 247
notebook. The calculations
on
[p. 53]
are
related
to
the
material
on
[pp.
910]. The
square
brackets
on
this
page
are
in
the
original.
[101]The
following
is
a
derivation of
Poiseuille's law
for
the
laminar
flow
of viscous
fluids.
This
law
was
referred
to
earlier
in
connection with Knudsen's work
on
the molecular
flow
of
rarefied
gases; see
[p.
11].
The derivation
proceeds by looking
at
the frictional
force
exerted
on
a
small
cylinder
of radius
r
of
flowing
liquid
within the tube
which is
compensated
by
the
pressure
difference
along
the tube. For
a
similar
treatment
see,
e.g.,
Loeb
1927, pp.
243245.
R
is
the radius of the
tube,
u
is
the
flow
velocity
and
z
the coordinate
along
the
tube,
n
denotes
the friction
coefficient,
and
y
is
an
abbreviation for the
pressure gradient
dp/dz.
[102]This
relation
implies
the
boundary
condition that the
flow
velocity
vanishes
at
the
surface.
[103]The
factor of
8
in
the denominator should
be
4.
See note 29.
[104]In
the second
equality,
the relation
n
=

is
used,
which
was
derived
on
[p.
6] (where
R
is
used instead of
n).
The relation for the
mean
free
path is
derived
on
[pp.
45].
[105]Einstein
compares
Poiseuille's law with Knudsen's relation from
[p. 12].
Note that
c
=
y(3RT)/M.
[106]The
following
discussion of
probability concepts
should
probably replace
a
related
pas
sage on
[p.
16].
[107]The words
"(oo viele)" are
interlineated.