Determination of discharge during pulsating flow

Abstract

Pulsating flow in an open channel is a manifestation of unstable-flow conditions in which a series of translatory waves of perceptible magnitude develops and moves rapidly downstream. Pulsating flow is a matter of concern in the design and operation of steep-gradient channels. If it should occur at high stages in a channel designed for stable flow, the capacity of the channel may be inadequate at a discharge that is much smaller than that for which the channel was designed. If the overriding translatory wave carries an appreciable part of the total flow, conventional stream-gaging procedures cannot be used to determine the discharge; neither the conventional instrumentation nor conventional methodology is adequate. A method of determining the discharge during pulsating flow was tested in the Santa Anita Wash flood control channel in Arcadia, Calif., April 16, 1965. Observations of the dimensions and velocities of translatory waves were made during a period of controlled reservoir releases of about 100, 200, and 300 cfs (cubic feet per second). The method of computing discharge was based on (1) computation of the discharge in the overriding waves and (2) computation of the discharge in the shallow-depth, or overrun, part of the flow. Satisfactory results were obtained by this method. However, the procedure used-separating the flow into two components and then treating the shallow-depth component as though it were steady--has no theoretical basis. It is simply an expedient for use until laboratory investigation can provide a satisfactory analytical solution to the problem of computing discharge during pulsating flow. Sixteen months prior to the test in Santa Anita Wash, a robot camera had been designed .and programmed to obtain the data needed to compute discharge by the method described above. The photographic equipment had been installed in Haines Creek flood control channel in Los Angeles, Calif., but it had not been completely tested because of the infrequency of flow in that channel. Because the Santa Anita Wash tests afforded excellent data for analysis, further development of the photographic ,technique at Haines Creek was discontinued. Three methods for obtaining the data needed to compute discharge during pulsating flow are proposed. In two of the methods--the photographic method and the depth-recorder method--the dimensions and velocities of translatory waves are recorded, and discharge is then computed by the procedure developed in this report. The third method?the constant-rate-dye-dilution method--yields the discharge more directly. The discharge is computed from the dye-injection rate and the ratio of the concentration of dye in the injected solution to the concentration of dye in the water sampled at a site downstream. The three methods should be developed and tested in ,the Santa Anita Wash flood control channel under controlled conditions similar to those in the test of April 1965.