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Approximate methods in surge-tank calculations

Published online by Cambridge University Press:  24 October 2008

A. M. Binnie
A. M. Binnie
Affiliation:
The Engineering LaboratoryCambridge
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Extract

The equations of motion in a surge-tank fitted to a hydraulic pipe-line are non-linear. Various methods of solving them were described by Durand: (1) simplification of the equations and the use of empirical coefficients, (2) simplification by taking the friction forces as proportional to the first power of the velocity, (3) a step-by-step method of solution. As a revolt against the serious expense of time involved in (3) (which was later developed by Jakobsen and by Cole), he was led to devise other methods including the use of models, which he dealt with subsequently in more detail. Nevertheless, there remains a need for a quick approximate method of calculating the maximum surges which may be used with confidence at least in the early stages of design. A promising line of attack was suggested by the success which has attended the approximate analysis of mechanical vibrating systems having non-linear characteristics. This method has been set out by Den Hartog, who dismisses step-by-step solutions as ‘too laborious’.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 42 , Issue 2 , June 1946 , pp. 156 - 166
Copyright
Copyright © Cambridge Philosophical Society 1946

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References

* Durand, , Trans. American Soc. Mech. Engrs, 34 (1912), 319.Google Scholar

† E.g. Johnson, , Trans. American Soc. Mech. Engrs, 30 (1908), 443.Google Scholar

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§ Cole, , Sel. Engng Pap. Instn Civ. Engrs, no. 55 (1927)Google Scholar, to which an extensive bibliography is appended.

∥ Durand, , Trans. American Soc. Mech. Engrs, 43 (1921), 1177.Google Scholar

Hartog, Den, Mechanical Vibrations, 2nd ed. (McGraw-Hill, New York and London, 1940), p. 402.Google Scholar

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† Ibid. p. 409.

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* Privately communicated.