A Novel and Enhanced Calibration of the Tilting Weir as a Flow Measurement Structure

A large collection of laboratory measurements of piezometric head ($h$) and discharge ($Q$) were made over hydraulic models of a tilting weir at nine different angles, ranging from 25.7° to 90° within a 0.3-m-wide flume. These measurements were corroborated with additional laboratory data taken within a 1-m-wide flume across four inclination angles. The range of both inclination angle ($\theta$) and flow scale examined in this study elucidate the nature of the head-discharge rating equation beyond previous work. Results show that as $\theta$ decreases under a constant $Q$, the $h$ over the weir decreases in a monotonic fashion due to the shallower angle of attack of the flow, which results in less curvature of the streamlines over the crest and therefore less deviation from the upstream hydrostatic pressure condition. To incorporate this effect into the head-discharge rating equation, a transformation of the $h$ term was applied by multiplying the measured $h$ that occurs over a tilting weir by a correction factor to match the effective $h$ that would occur if the weir were aligned perpendicular to the flow at the same discharge. Thus, a modified form of the classical sharp-crested weir rating equation can be used as a means for determining the value of $Q$ for tilting cases to a high degree of accuracy. The degree of accuracy is dependent on dimensionless Reynolds and Weber numbers describing the flow inertia in the approach to the weir in relation to respective viscous and surface tension scale effects. This approach portends marked flow measurement enhancement for flow conditions above a suggested inertial threshold.

To achieve reliable and equitable water distribution, it is necessary to accurately estimate the volumetric discharge of water to flow through “rivers and canals.” One such method of accomplishing this is by using hydraulic structures, such as the tilting weir. This structure not only can be used to measure the discharge of water on a continuous basis, but also allows for regulating the water level upstream of the structure. Presently, tilting weirs are often used to control water levels, but the literature on their utilization as flow measurement structures has remained sparse. This study presents a thorough analysis of laboratory experiments on scaled models of tilting weirs, where the flow depth upstream of the structure and the inclination angle are used to calibrate an equation to estimate the discharge to a high degree of accuracy. Operational guidelines to ensure minimum uncertainty in measurement are also given.