<DOC>
<DOCNO>
1382
</DOCNO>
<TITLE>
the solution of the equations of the laminar boundary
layer for schubauer's observed pressure distribution
for an elliptic cylinder .
</TITLE>
<AUTHOR>
hartree,d.r.
</AUTHOR>
<BIBLIO>
arc r + m.2427, 1949.
</BIBLIO>
<TEXT>
  the solution of the equations of the laminar
boundary layer has been carried out for the pressure
distribution for an elliptic cylinder of axial ratio 2.96 ..  1 with
its major axis in the direction of the incident stream .
the solution has been obtained by the method of hartree and
womersley .  in applying this method the derivatives
parallel to the boundary are replaced by finite differences, so
that the partial differential equation of the boundary
layer is replaced by an ordinary equation relating the velocity
distribution through the boundary layer at one section
to that at another, at an interval upstream .  by two independent
integrations covering the same range by finite intervals
of different sizes, it is possible to estimate the errors
involved in replacing the derivatives by finite differences,
and so to correct for these errors .
  the process of solution requires the values of the pressure
gradient along the solid boundary, and there is a certain
tolerance in the derivation of the pressure gradient distribution
from a limited number of observed values of pressure .
an analysis of schubauer's pressure distribution is outlined, and
the results were used for the main solution calculated .
it is found that the solution, for the distribution of pressure gradient
so derived, does not give separation of the boundary
layer from the solid boundary, whereas the actual flow does separate .
  it is found that the calculated solution is very sensitive to
the pressure distribution, and a comparatively small
modification of the pressure distribution gives a solution which
does indicate separation close to the point at which
separation is observed to occur .  the solution with this pressure
distribution also gives very good agreement with the
observed velocity distribution through the boundary layer at
points upstream from separation .
</TEXT>
</DOC>
