Comment on “Measurement of Gravitational Acceleration Using Bernoulli’s Equation”

• John H. Lienhard, V ^[1] ; John H. Lienhard, IV ^[2]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
  2. [2] University of Houston

     University of Houston

     Estados Unidos

     
• Localización: The Physics Teacher, ISSN 0031-921X, Vol. 62, Nº. 6, 2024, págs. 421-421
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We read the paper by Jang et al.1 with great interest. The authors describe two elementary experiments for measuring the gravitation acceleration. The experiments are based on a jet of water flowing out of a hole in a tank. The authors concluded that their Experiment II was less accurate than their Experiment I. Here, we show that Experiment II gives results quite close to Experiment I if the data are reduced differently.

    Experiment II requires a value for the velocity coefficient of a sharp-edged orifice, cv. Jang et al. cite our 1984 paper,2 which applies viscous fluid flow principles to show that cv is very nearly equal to 1. In other words, cv ≅ 1. Our paper discussed in detail why the historical value of cv = 0.98 is not correct. So, we were surprised that Jang et al. used cv = 0.98 (from a handbook) to reduce the data in Experiment II.

    How does the difference in cv affect the results? From Eq. (16), the experimental value of g is proportional to (cv)−2. If we take cv = 1, instead of cv = 0.98, the reported experimental values (10.11 and 10.18 m2/s) are reduced to 9.71 and 9.78 m2/s. The reduced values differ from the official value in Daegu province (g = 9.7981 m2/s) by only −0.9% and −0.04%. Thus, Experiment II yields results comparable to Experiment I (9.84 ± 0.19 m2/s).

    Our 1984 paper focused on laminar boundary layer theory, so it is understandable that the authors may have preferred the handbook value of cv. However, the data from Experiment II should be reduced using cv = 1. With the correct cv, these experiments provide an excellent introduction to several aspects of elementary physics.