Size Scale Effects on Linear Weir Hydraulics

Linear weirs are a common hydraulic structure that have been used for centuries with many different applications. One characteristic of weirs that is particularly useful is the head-discharge relationship where the discharge over the weir is directly related to the upstream water depth above the crest. In general, the head-discharge relationship for a weir is determined experimentally in laboratories using geometrically similar models. Due to space, time, money, and discharge capacity limitations at water laboratories, creating full scale models is not always a feasible option when determining head-discharge relationships for large prototype weirs. It is typically more cost effective to create a scale model than to build a full scale model or conduct tests on the prototype. Because of this fact, physical modeling has been one the most important tools in determining head-discharge relationships for weirs. However, as the physical size of the model decreases, size scale effects associated with surface tension and viscosity forces can significantly affect the results from the physical model and cause the results to differ from what would actually occur at the prototype scale. Therefore, it is important to understand what affects surface tension and viscosity forces have on the head-discharge relationship for different size weirs and when those effects are no longer negligible. The purpose of this research was to evaluate size scale effects for linear weirs. Weirs models of three different crest shapes (flat-top, quarter-round, and half-round) were constructed and tested at four different geometrically similar sizes [weir heights (P) = 24-, 12-, 6-, and 3-in]. This was done in order to evaluate how size scale effects affect the head-discharge relationship as model size decreases for different crest shapes. Discharge coefficients were calculated for relative upstream head values ranging from 0.01 ≤ Ht/P ≤ 2.0 for vented and non-vented conditions. Nappe aeration behavior was documented and compared to determine where differences in the nappe trajectory occurred as a result of scale effects. Comparisons were made with data from others researchers to determine if the recommendations for minimum head limits were similar to the results from this study. This study examined the errors in the discharge coefficient associated with size scale effects and suggested limits to avoidance depending on model scale and crest shape