scholarly journals The axially symmetric potential flow about elongated bodies of revolution / by L. Landweber.

1951 ◽  
Author(s):  
L. Landweber ◽  
Keyword(s):  
Potential Flow ◽  
Axially Symmetric ◽  
Bodies Of Revolution ◽  
Symmetric Potential

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

Axially symmetric potential flow around a slender body

1967 ◽  
Vol 28 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Richard A. Handelsman ◽  
Joseph B. Keller
Keyword(s):  
Potential Flow ◽  
Slenderness Ratio ◽  
Strength Distribution ◽  
Point Sources ◽  
The Body ◽  
Linear Integral Equation ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Symmetric Rigid Body ◽  
Linear Integral

Axially symmetric potential flow about an axially symmetric rigid body is considered. The potential due to the body is represented as a superposition of potentials of point sources distributed along a segment of the axis inside the body. The source strength distribution satisfies a linear integral equation. A complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio ε½, which is the maximum radius of the body divided by its length. The expansion contains integral powers of ε multiplied by powers of log ε. From it expansions of the potential, the virtual mass and the dipole moment of the body are obtained. The flow about the body in the presence of an axially symmetric stationary obstacle is also determined. The method of analysis involves a technique for the asymptotic solution of integral equations.

scholarly journals Some axially symmetric potential problems

1972 ◽  
Vol 18 (1) ◽  
pp. 55-76 ◽  
Author(s):  
F. G. Leppington ◽  
H. Levine
Keyword(s):  
Integral Equation ◽  
Asymptotic Expansion ◽  
Integral Equations ◽  
Asymptotic Estimate ◽  
Axially Symmetric ◽  
Primary Interest ◽  
Symmetric Potential ◽  
Approximate Integral ◽  
Potential Problems ◽  
Higher Order Terms

AbstractSome axially symmetric boundary value problems of potential theory are formulated as integral equations of the first kind. In each case the kernel admits an expansion, for small values of a parameter of the problem, that leads to an approximate integral equation whose solution provides a direct asymptotic estimate for the physical quantity of primary interest. A manipulation of the original and modified integral equations provides an efficient formula for calculating higher order terms in the asymptotic expansion.

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