Potential flow in engine valves Page: 7 of 29
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N.A.C.A. Technical Memorandum No. 343
Zr + o'2 K + 1
-Z' +" 0
or with the insertion of = 2 and -2
z = - w 2 or, since z = e(P+i,
w* + pw* + 1
w4 + \w2 + 1
The importance of . is due to the fact that the points
+p ii = c' must have known velocity values. With this con-
dition, we find that p = - 2 cos 2a,. in which a is the
Ingle formed by the stream in infinity with the x axis.
The parameters occurring in the solution, with which we
can satisfy the prescribed geometric conditions of flow, are
especially important. It is obvious that they must be connect-
ed with the physical properties of the flow. It is in fact ap-
parent from equation (1) that only the two following parame-
1. The ratio of the velocities at A cand 0 equals K ;
2. The angle a, which the stream in infinity forms with
the x axis.
Since the three quantities b, h and r = BC must be deter-
mined, only the relations n = h/b and m = r/b - 1, obtained
by two integrations, can be involved. The relation between
w and x is established through equation (1). From dx w
it follows that dz dx and z = dx dw, which is simpli-
w dw w
Here’s what’s next.
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/7/: accessed October 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.