Potential flow in engine valves Page: 6 of 29
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N.A.C.A. Technical Memorandum No. 343 5
w' = W + 1 C' dz'
z C + B'
an assertion which can be easily verified by remembering that
dw' - 1
dz' (z' + t )1/2 (z' - ()1
is increased by rr/2 at the points +bo. After determining
the constants, we obtain
z' = 1/2 w + 1
Plotting the potential on the half-plane.- The boundary
lines PBCD and AED form streamlines between which the whole
stream flows (Fig. 5). The potential is thus plotted on a
strip #B - tE . This difference is, at the same time, the
amount of the fluid flowing through. In order to have a defi-
nite case in mird, we put ta - *E = i. By means of
z = e?+i: this strip is plotted on the half-plane, so that
z = B comes after -1, A comes after 0 and D remains in
If we now establish, by a linear transformation, a connec-
tion between the two half-planes, so that corresponding points
coincide, we obtain the function x = f w. In the expression
z = z'b + a we determine the constants a, b, c, so that
z' = B after -i and z' = A = - 1/2 (K + after
z = 0 and thus obtain
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/6/: accessed April 27, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.