Potential flow in engine valves Page: 8 of 29
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N.A.C.A, Technical Memorandum No. 343
flied by the elimination of dx, since dx/dw is known.
4 2 4w +2X 4w +2 + (2)
Z = der - f(2)
W w + kw2 + 1 w1 w4 + vlW + 1
Zero and unity are the integration limits for r and h.
K2 - 1+ 1 + cosc
r 2 K arc tanK + K + cosalog 1 - os- sin
K2 + 1 1 +K U 1 + sinx
h = i K log - + -+ i cosB - sina log 1 sina
For the relations m - b - 1 and n = b, we obtain, by
taking into consideration for ho = b + i h only the imaginary
1 - K* o 1 + cost
= 2 re tnK log cos sina(3)
rrtu 1 - cos
n = log + K Co - co s lo1g na sino (4)
TT1 - K T 1 - sina
Equations (3) and (4) represent the solution of the first
problem. They always go together, so that here we have a set
of equations with three unknown quantities. If, for example,
an overlapping m is stipulated, m must be introduced into
equation (3), then the values of K and a which satisfy equa-
tion (3) must be determined and then these values must be in-
troauced into equation (4), from which we obtain the valve-
lift n. This procedure must be followed for all values of
la which satisfy equation (3).
Such a computation would be very tedious and the determi-
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Eck, Bruno. Potential flow in engine valves, report, December 1, 1925; (digital.library.unt.edu/ark:/67531/metadc65148/m1/8/: accessed June 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.