ON THE BEHAVIOR OF SMALL DISTURBANCES TO POISEUILLE FLOW IN A CIRCULAR PIPE,
Abstract
A simple, but crude, analysis shows among other things that the radius at which the disturbance velocity is a maximum is roughly that at which the velocity of the Poiseuille flow is equal to the frequency, f, times the disturbance wavelength. Eigenfunctions are found precisely for the two limiting cases in which, as f a to the 2nd power/v tends to infinity, the disturbance becomes confined to a thin layer situated (a) near the centre of the pipe, and (b) near the wall. The eigenfunctions are presented graphically in such a way that immediate comparison can be made with some of Leite's experimental results. Good agreement is found. Possible changes in the form and apparent damping rate of a disturbance are discussed in terms of a particular case. Next, an asymptotic procedure is carried out, which proves to give a good approximation to the eigenvalues and eigenfunctions over a wide range of conditions. For simplicity, the calculations are carried out for the case in which the Reynolds number is infinite, so that the eigenvalues depend only on f a to the 2nd power/v. For each mode it is found that the damping rate is an increasing function of the frequency for high frequencies, but as the frequency is decreased the damping rate approaches a limiting value.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 12, 1964
- Accession Number
- AD0613131
Entities
People
- A. E. Gill
Organizations
- University of Cambridge