<DOC>
<DOCNO>
155
</DOCNO>
<TITLE>
on the solution of the laminar boundary layer equations .
</TITLE>
<AUTHOR>
howarth,l.
</AUTHOR>
<BIBLIO>
proc.roy.s.a, 164, 1938, 547.
</BIBLIO>
<TEXT>
the problem of the flow along a flat plate
placed edgewise to a steady stream,
when a retarding pressure gradient
varying linearly as the distance x
from the leading edge of the plate
is superposed is discussed .  if y denotes
distance measured perpendicular to
the plate, a solution is obtained in the
form of a power series in x where
coefficients are functions of .  differential
equations are obtained for these
coefficients .  seven of the coefficients
have been obtained with reasonable
accuracy, and the eighth and ninth
roughly .  unfortunately it appears
that about eight more terms are
required to carry the solution to
the point of separation,. the work
involved in their determination is
prohibitive .  two approximate methods
have been developed for determining
the error when the first seven terms
of the series are used as an approximation .
these methods lead to the
determination of the point of separation
and are in agreement as to its
position .  if is the velocity at the
edge of the boundary layer at the
leading edge of the plate and is the
velocity gradient, separation is found
when .  a method is
developed for the solution of the
boundary layer equations in any retarded region .
it is obtained by replacing
the velocity distribution at the edge
of the boundary layer by a circumscribing
polygon of infinitesimal sides and
applying the preceding solution
to each of these sides, making the
momentum integral continuous at each
vortex .  the problem is thereby
reduced to the solution of a first order
differential equation .
</TEXT>
</DOC>
