A Comparison of Two Methods for Deriving the Differential Equation of Oscillation of an Ideal Liquid in Communica-tion Tube with Different End Cross Sections

Liu Hsien-chih

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1980 > 1(3): 301-310

Liu Hsien-chih. A Comparison of Two Methods for Deriving the Differential Equation of Oscillation of an Ideal Liquid in Communica-tion Tube with Different End Cross Sections[J]. Applied Mathematics and Mechanics, 1980, 1(3): 301-310.

Citation:

PDF( 2700 KB)

A Comparison of Two Methods for Deriving the Differential Equation of Oscillation of an Ideal Liquid in Communica-tion Tube with Different End Cross Sections

Liu Hsien-chih

Shantung Institute of Technology

Received Date: 1980-02-20
Publish Date: 1980-06-15

Abstract

Abstract

Possibly not shorter than a half century, there has been ezisting a method for deriving the differential equation for the oscillation of an ideal liquid in communication tube with different end cross sections in the scientific literature, which,according to our opinion, is somewhat defective. With this paper we present another derivation in aiming to make possibly a convincing comparison. Our method leads to results from which the three different laws for vibration period setting up in the antiquity by Isaac Newton, Johann Bernoulli and Danielis Bernoulli can be degenerated outcomes.

FullText(HTML)

References(9)

References

[1]	Newton,Isaac,Plzilosophioe Naturalis Prineipia Mathenaatiea, London 1687.
[2]	Bernoulli,Johann,Commentarii Academiae Seientiarum Petropolitanae,1727.
[3]	de Lagrené,H,,Gours de Navigation intérieure,Paris, 1869.
[4]	Bernoulli,Danielis, Hydrody;amica (Argentorati,1738).
[5]	Liu Hsien-Chih(刘先志),Beitrag zur Kenntnis der Eigensch wingung einer idealen Flüssigkcit in kommunizierenden Rohren,ZAMP, IV,1953.
[6]	Wittenbauer, F.,Aufgaben aus der Teehnischen Mechanik,Ⅲ.Band, Julius Springer,Berlin 1921.
[7]	Liu Hsien-Chih(刘先志)Eigensch wingungen einer idealen Fliissigkeit in Rohrleitungen mit verschiedenen Endquerschnitten,Ing,-Archiv,1952.
[8]	Liu Hsien-Chih(刘先志),Über schwingungen einer idealen Fliissigkeit in ellipsen-and kreisbogéniörmigen,kommuniziercnden Röhren, Ing.Archiv,1952.
[9]	A Handbook on Torsional Vibration,B.I.C.E.I2.A,,Cambridge University Press, 1958.