## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. 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.
Journal Article

# 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
Stable URL: http://www.jstor.org/stable/43634080
Page Count: 8
Were these topics helpful?

#### Select the topics that are inaccurate.

Cancel
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.
Preview not available

## 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.

• [377]
• 378
• 379
• 380
• 381
• 382
• 383
• 384