234 DOC.
39
THEORY OF WATER WAVES
Doc.
39
Elementary Theory
of
Water
Waves
and
of
Flight
by
A.
Einstein,
Berlin-Wilmersdorf
What
accounts
for the
carrying capacity
of
the
wings*
of
our flying
machines and
of
the birds
soaring through
the air in their
flight?
There is
lack
of
clarity
on
this
question.
I must
confess that
I
could not find
anywhere
in the
specialized
literature
even
the
I
hope, therefore,
to
give
some
pleasure
when
I
try
to
remedy
this
deficiency
with the
following
short consideration
on
the
theory
of
the motion
of
liquids.
Let
an
incompressible liquid
with
negligible
inner
friction stream
in
the direction
of the
arrows through a pipe
that
is
tapering
off
to
the
right (Fig.
1).
distribution of the
pressure
in the
pipe.
Since the
same
quantity
of fluid
per
second
Fig.
1.
must flow
through every
cross section,
the
velocity
of flow
q
must
be
the lowest at
the
largest
cross
sections and the fastest
at
the
smallest
cross
sections. The velocities
of
the
particles
of
the
liquid
will therefore
be smallest at
L
in
Fig.
1
and will
continuously
increase toward
R.
This acceleration
of
the
particles
of the
liquid can only
be effected
by
the
pressure
forces that act
upon
them. In order for the
cylindrical liquid particle
F
to execute
an
accelerated
movement
toward
the
right,
its
rear-end surface
A must
be
under
a higher pressure
than its front-end surface
B.
The
pressure
at
A
exceeds the
pressure
at
B. Repeating
this
conclusion,
it follows that the
pressure
within the
pipe
decreases
from
L
to
R.
The
same
distribution of
pressure (decrease
of
pressure
from L to
R)
is found
in
an
analogous
consideration
if
the direction
of
flow
of
the
liquid
is reversed.
In
generalizing,
we
can
state
the
following long-known
theorem
of
the
hydrodynamics
of fluids without friction.
When
we
path
of
a
liquid
particle
in
a
stationary flow,
we
find the
pressure p always
larger
where the
velocity
q
is
lower and vice
versa.
This theorem is
quantitatively expressed
for
noncompressible liquids by
the well-known
equation
*Translator's
of
the basic term
Auftrieb
=
wing lift,
Einstein
uses
the
extremely complex concept
of
Tragfähigkeit
der
Flügel
=
carrying capacity
of
wings,
which
linguistically
and
falsely suggests
in German
a
rather
elementary
quantity-at least to the
layman.
The R.
v.
Mises
lectures
in
Fluglehre,
which in
part
date
back
to
1913,
represent
the state
of
the art at the time
of
Einstein's
article;
they
were
later
incorporated
into the
Theory
of
Flight
(Dover
reprint,
1945 &
1959).
[1]
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