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Refraction through cylindrical tubes

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Abstract

When viewed from the outside, objects placed inside containers with cylindrical walls (i.e. test tubes, beakers, pipes) appear distorted because of the curvature of the interfaces and the differing refractive indices of the media. We have developed a method for measuring the coordinates of a particle located inside a straight cylindrical tube by viewing it from two directions using a camera. A set of equations is derived which maps all points inside the tube to the camera image plane; ray tracing diagrams are shown for several important cases, indicating variable distortion, hidden regions, multiple images, and critical reflections. An experimental test was performed to check the calculations; excellent verification was obtained.

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References

  • Agrawal, Y.; Talbot, L.; Gong, K. 1978: Lase anemometer study of flow development in curved circular pipes. J. Fluid Mech. 85, 497–518

    Google Scholar 

  • Ahmed, S. A.; Giddens, D. P. 1983: Flow disturbance measurements through a constricted tube at moderate Reynolds numbers. J. Biomech. 16, 955–963

    Google Scholar 

  • Bicen, A. F. 1982: Refraction correction for LDA measurements in flows with curved optical boundaries. TSI Quarterly 8, 10–12

    Google Scholar 

  • Boadway, J. D.; Karahan, E. 1981: Correction of laser Doppler anemometer readings for refraction at cylindrical interfaces. DISA Inf. 26, 4–6

    Google Scholar 

  • Bovendeerd, P. H. M.; Van Steenhoven, A. A.; Van de Vosse, F. N.; Vossers, G. 1987: Steady entry flow in a curved pipe. J. Fluid Mech. 177, 233–246

    Google Scholar 

  • Durrett, R. P.; Gould, R. D.; Stevenson, W. H.; Thompson, H. D. 1985: A correction lens for laser Doppler velocimeter measurements in a cylindrical tube. AIAA J. 23, 1387–1391

    Google Scholar 

  • Jenkins, F. A.; White, H. E. 1976: Fundamentals of optics, pp. 115–126. New York: McGraw-Hill

    Google Scholar 

  • Lowe, M. L.; Kutt, P. H.; York, T.; Kazanov, L. A.; Leavy, B. 1992: Reconstruction of three-dimensional particle trajectories in flows through curved circular tubes. To be published in Experiments in Fluids

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Authors and Affiliations

  1. Physics Department, Loyola College, 21210, Baltimore, Md., USA

    M. L. Lowe

  2. Physics Department, Univ. of Pennsylvania, 209 S. 33rd Street, 19104, Philadelphia, Pa., USA

    P. H. Kutt

Authors
  1. M. L. Lowe
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  2. P. H. Kutt
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Lowe, M.L., Kutt, P.H. Refraction through cylindrical tubes. Experiments in Fluids 13, 315–320 (1992). https://doi.org/10.1007/BF00209503

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  • DOI: https://doi.org/10.1007/BF00209503

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