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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Additional info for Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow
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.