Application of the Law of Kinematic Similitude to the Surge-Chamber Problem

Abstract

Abstract The problem of the hydraulic surge chamber gives rise to certain differential equations which do not admit of solution in analytical form. Under these conditions, various modes of treatment have been proposed. The present paper develops and describes a comprehensive experimental method utilizing the law of kinematic similitude. By this method a laboratory model of convenient dimensions is set up and subjected to a program of operation corresponding to that for the field installation. The movements of water level, times, etc., as measured for the model, are then multiplied by suitable relation factors, thus giving the results to be anticipated for the field installation. The model may thus, in a sense, be considered as a form of mechanism which solves the equations as applied to the model form, and these results multiplied by suitable relation factors give the corresponding results to be anticipated in the field case. The principal advantages of the model method are as follows: 1 The model is simple and readily set up. Once in operation, the most varied conditions may be quickly examined, thus making possible a range of examination in detail, the extent of which would be quite impracticable by any methods of numerical computation. 2 In all analytical methods of treatment, pipe-line friction has been assumed to vary with the square of the velocity. In the model method the friction may be taken to vary with vn, where n is usually found to be about 1.85. 3 In analytical methods the surge chamber is usually taken as uniform in cross-section. With the model, the chamber may be of any form whatever. 4 The model method is readily extended to the case of a surge chamber with spillway or to the case of multiple chambers on one pipe line. 5 The model method provides readily for the examination of periodic fluctuations in power demand, of any amplitude and any periodicity. The examination of such fluctuating programs is beyond practical reach by numerical methods.