Improved calibration of Cutthroat flumes
An analysis of laboratory data for a 0.914-m (3-ft) length Cutthroat flume with four different throat widths is presented. Significant differences with previously published calibration parameters were found. Special attention was given to non-hydrostatic pressures at the upstream and downstream piezometer taps, and the variations are presented in a series of three-dimensional plots. Variation in relative pressure at different tap heights was observed and was concluded to represent a shift from a concave to a convex flow profile between the 0.305- and 0.203-m throat widths. This significant alteration in the flow profile correlates with a sharp change in the nf calibration parameter, describing a non-linear relationship with flume throat width. Alternative equation forms were explored in an attempt to increase the predictive accuracy of the calculated flow rates for free- and submerged-flow regimes. The alternative equations showed a decrease in the percent error, in the submerged-flow regime, by more than 50%. Transition submergence was observed to vary not only due to flume size, but also to flow rate. An empirically fitted equation was developed to calculate the transition submergence as a function of throat width and flow rate. In addition, a separate calibration for free-flow parameters was defined based on measurements from an upstream point gauge. The flow measurement accuracy of existing Cutthroat flumes can be significantly increased, especially for submerged-flow regimes.
Generic Free-Flow Rating for Cutthroat Flumes
Computational fluid dynamics (CFD) software was used to generate water depth and discharge data for 51 Cutthroat flume sizes, including all 24 standard sizes published by the flume's developer and 27 intermediate sizes. The hydraulic model was validated by using data from several sources, including physical model testing for 15 standard sizes and three intermediate sizes. Grid-size independence was also confirmed for a range of computational cell sizes and the calibration results for 15 standard flume sizes were compared with previously published calibration parameters. Through the validated CFD simulations, a full set of calibration and validation data was generated for each of 51 flume sizes, filling the gaps in the experimental data and permitting a full analysis of the performance of the flume. The study resulted in a generic calibration for free-flow conditions for any Cutthroat flume in the dimensional range of the 24 standard sizes and specified dimensional ratios according to the original design criteria. The error in the predicted discharge for all flume sizes is less than 3% of the full-scale discharge. DOI: 10.1061/(ASCE)HY.1943-7900.0000732. © 2013 American Society of Civil Engineers. CE Database subject headings: Flow measurement; Flumes; Canals; Calibration; Computational fluid dynamics technique. Author keywords: Flow measurement; Flumes; Cutthroat flume; Canals; Calibration.
Brauer groups of genus zero extensions of number fields
We determine the isomorphism class of the Brauer groups of certain nonrational genus zero extensions of number fields. In particular, for all genus zero extensions E of the rational numbers Q that are split by Q(√2), Br(E) ≅ Br(Q(t)).