Bergman’s Linear Integral Operator Method in the Theory of by M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M.

By M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M. A. (Math., Stanford), M. S. (Appl. Math., Brown) M. Aer. En. (Brooklyn), Dipl. Ing. (Lemberg) (auth.)

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By varying the constants Av, 1J = I, 2, ... , flows around various shapes can be obtained. On the other hand, it is often necessary to determine constants Av to yield a flow which approximates 4 S. Bergman: The approximation of function satisfying a linear partial differential equation. Journal, Vol. 6 (1940), pp. 537-561. 5 S. Bergman: Methods for determination and computation of flow patterns of a compressihle fluid. N. A. C. , T. N. No. 1018 (1946). 42 IV. Transonic Flow that about a prescribed boundary curve, the equation of which is, say, F (x, y) = o.

10) seems to be valid: T=[~ (l_h2 /'IAI '/'+ ... ]0) 30 III. 8), we have: 8=[! '/a[! (k+1)(k+l) + ... '/3+ ... 2. 5) a choice of parameters that leads to the asymptotic behavior of the physical gas for M = 1, i. 5) with !. For this value of (2. 3. 8) takes the different form: 2)-I. 12) 2 D (1 - L ( 2)-I. 13) D S-l (1 - 82 ( one gets: dL de = ! Suppose we fix y so that D = y6 = 0,606; this choice leads to curves that agree with the corresponding curves for a physical gas quite well for higher Mach numbers.

Sci. 6, 399-407 (1939). 26 II. Simplified Pressure-Density Relation ° obtain a better agreement between the hypothetical and the physical gas. :.. 5) 8'/(2~) y-l/~, (2 0)-1 y-l/~ 8'/(2~)-1~. de On the other hand, equation (1. 6) (section 1. 2) lead to ~~ = + 12- ~: = 0, and thus P )-'/2 q (drIe = (1 - 82 122 )'1" we h ave = 12 q-l 8. From the Bernoulli equation we have q ~~ d)' d)' dq dp S' . rIe o btam = --a;q rIe = - 8 q-2 de' mce M = 1 d)' M -2=_8(1_ 82 122)-1. 8), calculate M (12), i. , one of our desired relations between the variables of the gas.

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