DOC.
15
107
A,
B,
C
are
constants which
because of the
incompressibility
of the liquid
satisfy the condition
(2)
A
+ B + C
=
0
.
If,
now, a
rigid
sphere
of
radius
P
is located
at
point
x0, y0, z0,
the
motion
of the liquid around
it will
change.
We
will, for
convenience,
call
P
"finite"
and
the values
of
£,
7],
(, for which the liquid
motion
is
no
longer
noticeably
modified
by
the
sphere,
"infinitely
large."
Due
to
the
symmetry
of the
motion
of the
liquid,
it is clear that the
sphere
can
perform
neither
a
translation
nor
a
rotation
during
the
motion
considered,
and
we
obtain the
boundary
conditions
[8]
u
=
v
=
w
=
0
for
p
=
P
,
where
we
have put
p
=
U'2
+
j/2
+
£2
o
.
Here
u, v,
w
denote
the velocity
components
of the
motion
now
considered
(modified
by
the sphere). If
we
put
U
=
,
(3)
v
= Brj
+
,
iv
= C(
+
,
the velocities
u1,
v1,
w1
would have
to
vanish
at
infinity,
since
at
infinity
the motion represented in
equations
(3)
should reduce
to
that
represented
by
equations
(1).
The
functions
u, v,
w
have to
satisfy the
equations
of
hydrodynamics
including
internal friction
and neglecting
inertia.
Thus
the
following
equations
will
hold1:
[9]
1G.
Kirchhoff,
Vorlesungen
über
Mechanik.
26.Vorl.
[Lectures
on
Mechanics.
Lecture
26].
[10]