Effect of Tube Ovalling on Pressure Wave Propagation Speed

Abstract

For physiological and other flows it is often assumed that the pressure pulse wave speed is given by the classic Moens-Korteweg expression and this may be used, for example, to assist in the determination of in vivo blood vessel wall incremental Young's modulus. A number of physical factors affecting the value of this wave speed have been reviewed in the literature, but the effect of slight ovalling of the tube cross-section is rarely mentioned.

The analysis for a tube of elliptic cross-section shows that even a very small degree of ovalling can cause quite substantial reductions in Young mode wave propagation velocities compared with the classic Moens-Korteweg expression. Bending-induced changes in cross-section shape with internal pressure increase the apparent elasticity of the tube wall.

Experimental confirmation is provided by waterhammer wave speed measurements in a copper tube that has been ovalled by coiling. Even though the Young mode is not dominant in this case, as it would be for a physiological case, the measured wave speed is quite clearly less than the Moens-Korteweg theory and it can be shown that the small degree of measured tube ovality explains this.

Get full access to this article

View all access options for this article.

References

Lambossy

Aperçu historique et critique sur le, problème de la propagation des ondes dans un liquide compressible enfermé dans un tube élastique. Helv. Physiologica et Pharmacologica Acta, 1950, 8(2), 209–227; 1951, 9(2), 145–161.

Wood

F. M.

History of waterhammer. Civil Engineering research report 65, April 1970, Queens University, Kingston, Ontario.

Anderson

Menabrea's note on waterhammer; 1858. ASCE Proc., J. Hydraulics Div,, 1976, 102(HY1), 29–39.

Anderson

On the formulation of problems in hydraulic transients. PhD thesis, 1976, ch. 2, University of Aberdeen.

Raabe

Hydro power. The design, use and function of hydro-mechanical hydraulic and electrical equipment, 1985, Sec. 8.3 (VDI Verlag, Dusseldorf).

Evangelisti

Waterhammer analysis by the method of characteristics. L'Energia Elettrica, 1969, 46, (10), 673–692; 46(11), 759–771; 46(12), 839–858.

Wylie

E. B.

Streeter

V. L.

Fluid transients, 1983 (FEB, Ann Arbor, Mich.).

McDonald

D. A.

Blood flow in arteries, 2nd edition, 1974, Ch. 10 (Edward Arnold, London).

Korteweg

D. J.

über die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Röhren. Annln der Physik und Chemie (Wiedemann), Neue Folge, 1878, 5(12), 525–542.

10.

Parmakian

Waterhammer analysis, 1955, Chs 2 and 3 (Prentice-Hall, New York).

11.

de Almeida

Betamio A.

Manual de proteccão contra o golpe de ariete em condutas elevatorias, 1981, See. 8 (LNEC, Lisbon).

12.

Nakoryakov

V. E.

, Waterhammer and propagation of perturbations in elastic fluid-filled pipes. Fluid Dynamics (Consultants Bureau, New York), 1977, 11, 493–498.

13.

Thorley

A. R. D.

Guymer

Fundamental equations governing pressure surge phenomena in pipes of rectangular cross-section. Proc. Instn Mech. Engrs, 1975, 189(40), 325–332.

14.

Thorley

A. R. D.

Twyman

J. W. R.

Propagation of transient pressure waves in a sodium-cooled fast reactor. In Second International Conference on Pressure surges, London, September 1976, paper A1 (BHRA Fluid Engineering, Cranfield).

15.

Timoshenko

Strength of materials. Part I. Elementary, 3rd edition, 1955, Chs 11 and 12 (van Nostrand Reinhold, New York).

16.

Jahnke

Emde

Funktionentafeln mit Formeln und Kurven, 3rd edition, 1938 (Teubner, Leipzig and Berlin).

17.

Abramowitz

Pocketbook of mathematical functions, 1984 (Verlag Harri Deutsch, Frankfurt am Main).

18.

Gradshteyn

I. S.

Ryzhik

I. M.

Table of integrals, series and products (Ed. Jeffrey

), 4th edition, 1965 (Academic Press, New York).

19.

Wood

D. J.

Stelson

T. E.

Energy analysis of pressure surges in closed conduits. In Developments in theoretical and applied mechanics, Vol. 1, 1963, pp. 371–388 (Plenum Press, New York).