Potential flow in engine valves Page: 4 of 29
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J.C ,A Technical Memorandum No. 343
the velocity on the boundary is assumed to fall discontinuously
to zero.* If there is a pressure po in the still fluid, it
follows from Bernouilli's equation that the velocity is constant
on th3 free surface.. If we put this velocity = 1, it denotes
no specialization, but only a simplification of the calculation,
&hich can be offset by a suitable disposition.of the mass units.
From C, through D = m, up to E, the velocity is there-
fore 1, while from the point B, the pressure increases from
o to 1.
If the potential function of the flow sought is designated
by x = c + it, than dx/dz = u - iv = w represents the ve-
locity, the direction of the motion being reflected on the x
Since w for the margin of the flow is known partly by the
absolute magnitude and partly by the direction, we can deter-
mine the limits of the r plane (Fig, 2). At B, w = 0 and
at C the free surface begins (ice., w = i), so that the lim-
its of the free surface must lie on the unit circle and de-
* You are here referred to the valuable works of Sir G. Green-
hill, British Advisory Committee for Aeronautics, No. 19, 1910,
"Theory of a Streamline Past a Plane Carrier and of the Discon-
tinuity Arising at the Edge," which gives quite a complete list
of all the kinds of flow occurring in this field, along with
their diagra,Lmatt~ treatment
R. von Mises ("Zeitschxift des Vereines Deutscher Ingenieure,"
1917, pp. 447 ff, "Berechnung von Ausfall und Ueberfallzahlen")
hid previously discussed this problem thoroughly and had in
fact, calculated the coefficients for the form of flow here con-
Il_* - - -- - - - - - -
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/4/: accessed July 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.