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SIMILARITY LAWS FOR SUPERSONIC FLOWS

D. C. PACK and S. I. PAI
Quarterly of Applied Mathematics
Vol. 11, No. 4 (JANUARY, 1954), pp. 377-384
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43634080
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
SIMILARITY LAWS FOR SUPERSONIC FLOWS
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Abstract

The non-linear differential equation for the velocity potential of three-dimensional steady irrotational supersonic flow past wings of finite span has been investigated. It is found that the whole Mach number range from 1 to ∞ may be divided into two regions (not strictly divided), in each of which similarity laws are obtained, with two parameters ${K_1} = {\left( {{M^2} - 1} \right)^{\frac{1}{2}}}/{r^n}$ and ${K_2} = A{\left( {{M^2} - 1} \right)^{\frac{1}{2}}}$ ; τ is the non-dimensional thickness ratio, A the aspect ratio of the wing, M the Mach number of the uniform stream in which the wing is placed. The factor n is given explicitly as a function of M and τ; in the lower region of Mach numbers it tends to 1/3 as M → 1, for all τ, giving the ordinary transonic rule, and in the upper region it tends to -1 as M → ∞, for all τ, as in the ordinary hypersonic rule. It is shown that both two-dimensional flow and flow over a three-dimensional slender body, including axially symmetrical flow, are special cases of the present analysis, involving only one parameter K₁ in the similarity rules.

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