doi: 10.7763/IJAPM.2013.V3.229
The Construction of an Integral Formula for Computing Cylindrical and Non-Cylindrical Flow in the Region Bounded by Two Coaxial Cylinders of Varying Radii
Vasos Pavlika
- SOAS, University of London, UK
Abstract
In this paper an integral formula will be derived that will compute the velocity of a non-cylindrical flow variation in swan neck ducts with prescribed flow characteristics. The flow can be characterized by the total head, <span id="cke_bm_423S" style="display: none"> </span><em>H</em><span id="cke_bm_423E" style="display: none"> </span>(<em>ψ</em>) a function of only the stream function, <span id="cke_bm_424E" style="display: none"> </span><span id="cke_bm_408S" style="display: none"> </span><span id="cke_bm_406S" style="display: none"> </span><em>ψ</em><span id="cke_bm_408E" style="display: none"> </span><span id="cke_bm_406E" style="display: none"> </span> (<span id="cke_bm_409S" style="display: none"> </span><em>x</em><span id="cke_bm_409E" style="display: none"> </span>, <em>r</em>) a<span id="cke_bm_410E" style="display: none"> </span>nd by the function <span id="cke_bm_417S" style="display: none"> </span><em>C</em><span id="cke_bm_417E" style="display: none"> </span>(<em>ψ</em>) which is a functio<span id="cke_bm_418E" style="display: none"> </span>n of the azimuthal (circumferential) component of velocity vector, u in cylindrical polar coordinates (<span id="cke_bm_429S" style="display: none"> </span><em>x</em><span id="cke_bm_429E" style="display: none"> </span>, <em>r</em>, ). The solution to the problem is given in terms of an integral formula based on Green’s first identit<span id="cke_bm_430E" style="display: none"> </span>y.<span id="cke_bm_407E" style="display: none"> </span>
Keywords
- Stokes stream function
- cylindrical flow
- non-cylindrical flow
- singular integral formula
How to Cite
Vasos Pavlika, "The Construction of an Integral Formula for Computing Cylindrical and Non-Cylindrical Flow in the Region Bounded by Two Coaxial Cylinders of Varying Radii," International Journal of Applied Physics and Mathematics, vol. 3, no. 5, pp. 316-323, 2013. https://doi.org/ 10.7763/IJAPM.2013.V3.229
Copyright & License
Copyright © 2013 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).