<DOC>
<DOCNO>
459
</DOCNO>
<TITLE>
on the solution of the laminar boundary layer equations .
</TITLE>
<AUTHOR>
tani,i.
</AUTHOR>
<BIBLIO>
j.phys.soc.japan, 4, 1949, 149.
</BIBLIO>
<TEXT>
  the theory of the laminar boundary layer
offers a means of determining the skin friction
under the assumption of a given velocity distribution
outside the boundary layer .  owing to the
mathematical difficulties, however, exact solutions
are possible only when the velocity distribution
is expressed as a simple function of the distance
along the surface .  more complicated velocity distributions
necessitate recourse to the method of
expansion in series or that of step-by-step calculations,
but the labor involved is too great for the
methods to be of practical use .  approximate
method due to pohlhausen (1921), which had long
been recommended for general use, gives a reasonably
accurate solution in a region of accelerated
flow, but recently its adequacy in a region of
retarded flow has been questioned .  separation of
flow may actually occur where the solution of
pohlhausen fails to give it .  more recently howarth
solution, which gives fairly reasonable results in
a region of retarded flow .
  howarth's solution essentially consists in solving
the boundary layer equations for the particular
case in which the velocity u outside the boundary
layer decreases linearly with the distance x measured
along the surface, and utilizing the solution
by replacing the actual distribution of u by a
circumscribing polygon of infinitesimal sides .
therefore, it is assumed that the velocity distribution
at any section depends on the velocity
gradient du/dx at that section only, being affected
by the conditions upstream only in so far as this
affects the momentum thickness 0 .  in other words,
the velocity distribution across the boundary layer
is determined by a parameter .
</TEXT>
</DOC>
