Effect of side contraction on long-throated flume calibration

Abstract: Long-throated flume has been widely used as a flow measurement structure in irrigation channel systems. The key element of the long-throated flume is a throat, the length of which is longer than one and one-half times of the upstream energy head referenced to the throat invert or crest. Measurement accuracy of this flume is based on an accurate prediction of head-loss. This long throat causes the streamlines to be straight enough to sufficiently approximate hydrostatic pressure distributions. Replogle proposed a mathematic model for discharge calculation of various kinds of measurement structures. It is claimed that the model can achieve an accuracy within 2% based on the results of laboratory studies (within the range 0/07 < H1/L < 0.7). However, the additional inaccuracy is associated with errors in measured water level, which can also be improved by proper design of stilling well. When the calibration error is combined with the measurement error, the resulting accuracy of the measurement can be lower than 5%. A series of experiments were carried out in China to verify the effectiveness of this structure. In this experiment, three sets of flume were used: 1) five trapezoid flumes with only side contraction; 2) five trapezoid flumes with only vertical contraction; 3) two flumes with both side and vertical contractions, one with a trapezoid cross section and one with a U-shaped cross section. For the five flumes with only side-contractions, four upstream converging rates (length to width: 2, 2.5, 3, and 4:1) were used. The downstream side expansion rate was the same for all fumes, namely EM′=6. An extra set of models was created from the set with an upstream converging rate of 3:1 by cutting off the half-length of the downstream diverging section. For vertical contraction experiments, the sill height was p1=p2=0.2 m. Four upstream vertical-converging rates (2, 2.5, 3, and 4:1, horizontal to vertical) were used, and the downstream vertical convergence rate remained fixed at EM=6. An extra set of model runs was created from the set with vertical-converging rate of 3:1 by cutting off the half-length of the downstream diverging section similar as with the side contracted flumes. For flumes with side and vertical converge, both trapezoid and U-shaped cross sections were tested. Laboratory experiments showed that the long-throated flume was an effective flow-measurement structure with simple shape, low head loss, high modular limit, high robustness and accuracy. The best side contraction rate and vertical rate was 1:3 for accurate field calibration. When designed properly, downstream water level did not influence measurement accuracy. This should be advocated in most irrigation canals. Based upon test results, a modification was made to the original head loss equation to further increase the calculation accuracy. A local head loss ΔHcon was introduced to the original model to account for the head loss associated with a side contraction. This included a local head loss parameter ci that was used to calculate this extra head loss at the entrance to the throat section. In this paper, the recommended ci value for side contraction rates of 1:2, 1:2.5 and 1:3 were 0.317, 0.263 and 0.203, respectively. For flumes with only one side contraction, the modified method reduced the calculation error from 9.59% to 4.14%. With this new energy loss, calculation accuracy was significantly improved for long-throated flumes with side contractions, this will be helpful for water management.