Potential flow in engine valves Page: 11 of 29
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N.A.C.A. Technical Memorandum No. 343
If we obtain, for example, a margin of the log w plane,
where the limits have no neighboring infinite streamlines,
then this naturally has no further physical significance, even
though it may still be of some interest as a theoretical func-
tion. Without continuing this discussion, it may be mentioned
that only one other flow is possible in the above case (Fig.
11). Here also the stream berds 900 at E and follows the
horizontal wall, which it leaves, however, at E' where the
free surface begins. The angle a' then gradually increases
until it reaches its maximum at D = . On the other side,
the angle decreases until it reaches the value a = 0 at C.
The mathematical treatment of the last two cases is very similar
and they will therefore be considered side by side. For the
purpose of distinguishing them, the first will be designated by
IIa, arid the second by IIb. The principle of the calculation
is essentially covered in Section 1, although the difficulties
are much greater here. It is easily seen that the velocity
range of IIa and IIb is represented by a "quarter-plane" (Fig.
12), which is out along the unit circle from C to F and back
to D. The angle CBF is the maximum angle a, The log w
plane is obtained in a corresponding manner (Fig, .13). The
difference between IIa and IIb consists in the fact that sever-
al conspicuous points are shifted, a circumstance which is
first manifested by the iagram of the potential half-plane on
the velocity-potential plane. The diagram of the log w plane
on the half-plane might even here be accomplished by the Chris-
Imui m uil II 11111 I I
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/11/: accessed April 27, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.