A method is presented for the hydraulic design and analysis of labyrinth weirs based upon the experimental results of physical modeling. Discharge coefficient data for labyrinth weirs with quarter-round and half-round crest shapes are presented for sidewall angles ranging from 6 to 35°. Cycle efficiency is also introduced as a design aid, which compares the hydraulic performance of different cycle geometries. Geometric parameters that affect flow performance are discussed. The predictive accuracy of the design method is evaluated through comparisons to previously published labyrinth weir head-discharge data. The companion paper examines nappe behaviors that affect flow performance and presents hydraulic design considerations specific to nappe characteristics.

Current hydraulic design/analysis literature for labyrinth weirs is limited to headwater ratio (total upstream head/height of weir) values less than 1.0. This study utilized physical and numerical models to expand the current hydraulic performance theory of headwater ratios up to 2.0 for labyrinth weirs. The physical and numerical data provide practical design guidance for high headwater ratios and indicate that the empirical discharge coefficient design curves developed by Crookston may be acceptable for headwater ratios up to 2.0 or more. This was accomplished by evaluating the effects of higher upstream heads for a labyrinth weir with a 15° sidewall angle. Physical modeling was conducted in a rectangular flume under controlled laboratory conditions using two geometrically similar labyrinth models. A total of 120 data points were collected over a range of upstream heads. In addition, a numerical model of one of the physical model geometries was conducted using commercially available computationa...

Nappe behavior should be considered in the design of labyrinth weirs to ensure hydraulic optimization and to account for potential vibrations, pressure fluctuations, noise, and flow surging. Information regarding nappe aeration conditions (clinging, aerated, partially aerated, and drowned), nappe instability, and nappe vibrations for trapezoidal labyrinth weirs on a horizontal apron with quarter- and half-round crests (6°≤ sidewall angle ≤35°) is presented. Corresponding headwater ratio ranges and hydraulic behaviors associated with nappe aeration conditions are documented and discussed to aid in labyrinth weirs design, including design options directly related to nappe behavior (e.g., crest shape, crest roughness, vents, nappe breakers, notches, and staged cycles). The effects of artificial nappe aeration (a vented nappe) on nappe behavior and discharge capacity are also discussed, including recommended placements of nappe breakers.

The interaction of nappes from adjacent weir walls near an upstream apex can cause local submergence, which reduces labyrinth weir discharge efficiency. Local submergence effects can cause the head-discharge relationships for labyrinth weirs of equivalent lengths but different cycle numbers to differ. Empirical labyrinth weir discharge coefficients implicitly account for apex effects and local submergence; however, the uncertainty associated with applying hydraulic design data developed from specific weir geometries to comparable but different labyrinth weir geometries is not well understood. This study investigates the concept of labyrinth weir nappe interference and identifies labyrinth weir flow characteristics that decrease discharge efficiency, including local submergence. Parametric methods for quantifying nappe interference region size as a function of weir geometry (e.g., sidewall angle and crest shape) and flow conditions (e.g., headwater and nappe aeration) are presented. A comparison be...

The discharge capacity and hydraulic efficiency of a labyrinth weir can be increased with an Arced cycle configuration. An Arced geometric layout for labyrinth weirs is presented, including nomenclature for arc-specific geometric variables. Discharge coefficients as a function of HT/P for half-round trapezoidal Arced labyrinth weirs with 6 and 12° sidewall angles are also presented. The hydraulic performance of the tested Arced labyrinth weir geometries is compared to Projecting and in-channel labyrinth configurations and to an arced weir (horseshoe weir) with a half-round crest, including the effects of approaching flow conditions and local submergence. Differences between geometrically similar and geometrically comparable Arced labyrinth weirs are identified and discussed.