Potential flow in engine valves Page: 3 of 29
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P.A.CA Technical Memorandum No. 343 2
the fixed walls very quickly set limits to the formation of the
The theory of discontinuity surfaces evolved by Kirchhoff
and Helmholtz is preferably employed for the solution of two-
aimensional problems of this kind. This theory does not re-
quire constancy of velocity at the points where the ordinary
theory would require a very high velocity, namely, near the
sharp corners of the body. The very great velocity would, ac-
cording to Bernouilli s equation, demand a very great negative
pressure at these points, which is probably not assumable from
the physical viewpoint for ordinary fluids. Therefore, in or-
der to harmonize such a solution with the reality, we can as-
sume that these points are shut out from the flow by a small
circle, or that any slight rounding would necessitate very great
but not infinitely great velocities. Kirchhoff stated the
mathematical methods for the convenient application of this
theory to similar special cases. These methods consist chiefly
in finding the conformable diagram of the hodograph on the
plane of the velocity potential, which is always successful Jwhen
the rigid walls are flat.
1. Stream freea~n both sides.- We will first consider a
flow (Fig. 1), whi 'h, coming from infinity (A), is confined by
the parallel walls AB and AE, breaks off at C and E, forms
a free surface and then extends to infinity at an angle a.
The stream is assumed to be confined by a free surface, i.e.,
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/3/: accessed May 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.