Experimental physical model studies of hydraulic structures are often conducted to replicate flow behavior that may occur at the prototype scale. Geometric similitude is most often maintained between the prototype and model when studying reservoir and open channel hydraulic structures to account for the dominant gravity and inertia forces while other fluid forces (e.g., viscosity,surface tension) are assumed negligible. However, as model size and/or upstream head decreases, other fluid forces can exceed the negligible level and influence model flow behavior. This phenomenon is referred to as size-scale effects and is one potential origin of error in predicting the prototype behavior through testing geometrically similar models. To extend the existing research of size-scale effects on nonlinear weirs half-and quarter-round trapezoidal labyrinth weirs and piano key weirs were fabricated at length ratios of 1, 2, 3, 6, and 12. The largest weir model for each weir type (i.e., a weir height of 36 in for labyrinth weir models and a weir height of 33 in for piano key weir models) served as the corresponding prototype.Weir models were hydraulically tested to assess differences among head-discharge relationships and flow behavior. Limiting criteria were recommended to avoid size-scale effects depending on the weir type and model size. The results of this study will help hydraulic modelers determine what limiting criteria should be met to avoid size-scale effects.

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.