An improved method for shallow water flow velocity measurement with practical electrolyte inputs

The measurement of shallow water flow velocity is of interest to hill-slope hydrology and soil erosion mechanics. Lei et al. [Lei, T., Xia, W., Zhao, J., 2005. Method for measuring velocity of shallow water flow for soil erosion with an electrolyte tracer. Journal of Hydrology 301, 139-145] proposed an electrolyte pulse method for the purpose but found that the velocity measured at short distances from the salt injector was not as well estimated as those further away from the injector, though it is desirable to estimate velocity at short distances for the purpose of portable device development. In this study, the system was improved over the previous development. An additional sensor was added at the salt injection location to register the input signal as the actual boundary condition function instead of using the pulse assumption. Two function forms, a Normal distribution function (Normal Model) and a Sine function (Sine Model) were suggested to approximate the measured boundary conditions. These two determined boundary models were used to fit the experimentally obtained data using the least square method to determine the model parameters of the boundary conditions. The determined Normal Model and the Sine Model were both used to solve the transport processes as the convolution integrals of the pulse response and the actually determined boundary functions, so as to determine the shallow water flow velocity. Laboratory experiments were conducted to get data to verify the proposed methods and computational procedures. The experiment device included a flume, 4 m long and 15 cm wide, a solute injector, a data logger for control and data acquisition and a computer with specially designed software for data measurement and velocity estimation. The experiments involved three flow rates (12, 24 and 48 L min(-1)) and three slope gradients (4 degrees, 8 degrees and 12 degrees). Six sensors were used to measure the solute transport processes at 5, 30, 60, 90, 120 and 150 cm from the location where the salt solute was injected into the water flow. The solutions of both the Normal Model and Sine Model fitted the measured data very well for all the experimental conditions. The velocities at different distances from the salt solution injector and under different flow rates and slope gradients, as computed by the two models were almost identical, which indicated the feasibility of the method and the computational procedures as well as the two suggested models for velocity estimation. The velocity values estimated by the Normal and Sine Models agreed also with those measured by using the floating objects and the volumetric method. These demonstrated the rationality of the improved methods for shallow water flow velocity measurement. The results will be useful to design a practical system for the measurement of shallow water flow velocity. (C) 2010 Elsevier B.V. All rights reserved.