A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.
This research was conducted in the Lower Ping River Basin downstream of the Bhumibol Dam and the Lower Wang River Basin in Tak Province, Thailand. Most of the tributary streams of the Ping can be considered as ungauged catchments. There are 10- pumping station installation at both river banks of the Ping in Tak Province. Recently, most of them could not fully operate due to the water amount in the river below the level that would be pumping, even though included water from the natural river and released flow from the Bhumibol Dam. The aim of this research was to increase the performance of those pumping stations using weir projects in the Ping. Therefore, the river analysis system model (HEC-RAS) was applied to study the hydraulic behavior of water surface profiles in the Ping River with both cases of existing conditions and proposed weirs during the violent flood in 2011 and severe drought in 2013. Moreover, the hydrologic modeling system (HMS) was applied to simulate lateral streamflow hydrograph from ungauged catchments of the Ping. The results of HEC-RAS model calibration with existing conditions in 2011 showed best trial roughness coefficient for the main channel of 0.026. The simulated water surface levels fitted to observation data with R2 of 0.8175. The model was applied to 3 proposed cascade weirs with 2.35 m in height and found surcharge water level only 0.27 m higher than the existing condition in 2011. Moreover, those weirs could maintain river water levels and increase of those pumping performances during less river flow in 2013.