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# Accession Number:

## AD0829877

# Title:

## CALCULATION OF UNSTEADY FLOWS DUE TO SMALL MOTIONS OF CYLINDERS IN A VISCOUS FLUID.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE

# Report Date:

## 1967-12-01

# Pagination or Media Count:

##
33.0

# Abstract:

## The specific problem of interest concerns small sinusoidal vibrations of a ribbon of finite width 2a, but negligible thickness, moving normal to itself in a viscous fluid, and the final result of this report is a numerical solution for the force components added mass and damping coefficients on the ribbon. Care is taken with the numerical solution to ensure a correct treatment of the singularity at the edges of the ribbon, and also to seek a result which is of uniform accuracy with respect to the frequency sigma of oscillation. Although the above is the problem of most direct interest and was studied because of possible application to prediction of the effect of bilge keels on ships, a more general formulation is used to derive an integral equation, which is solved numerically only for the above special case. By use of Laplace transforms and a version of Greens theorem, the initial-value problem for arbitrary small motions of a deformable cylinder of arbitrary cross-section is reduced to solution of coupled integral equations, the unknowns being the pressure and vorticity distributions on the cross-section. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#