Minimum Specific Energy and Critical Flow Conditions in Open Channels

In open channels, the relationship between the specific energy and the flow depth exhibits a minimum, and the corresponding flow conditions are called critical flow conditions. Herein they are reanalyzed on the basis of the depth-averaged Bernoulli equation. At critical flow, there is only one possible flow depth, and a new analytical expression of that characteristic depth is developed for ideal-fluid flow situations with nonhydrostatic pressure distribution and nonuniform velocity distribution. The results are applied to relevant critical flow conditions: e.g., at the crest of a spillway. The finding may be applied to predict more accurately the discharge on weir and spillway crests.     

Transition Effects in Flow Over Side Weirs

The effect of water surface slope in the lateral direction on flow over side weirs was studied. Water surface elevation on the weir plane was expressed by a parameter ψ based upon the hydraulic profile on the channel axis. Two different relationships of ψ as a function of the Froude number were used to calculate side weir discharges. Results were compared with the experimental data. It was shown that better results are obtained when transition conditions of ψ = 1 at the ends of the side weirs with no lateral surface slope are taken into account. However the effect of water surface slope in lateral direction is of secondary importance as compared to the angle of the deflected water jet along the side weir.     

Experiments on Discharge Equations of Compound Broad-Crested Weirs

A linear combination of traditional discharge equations for simple rectangular and/or triangular weirs is proposed to describe the discharge equations of compound broad-crested (CBC) weirs. The CBC weirs are composed of rectangular, triangular, and/or truncated triangular weirs. Dimensionless discharge equations have been also derived. Laboratory experiments on discharge relations for flows over four CBC weirs were conducted in this study in order to calibrate the proposed discharge equations. The experiments were carried out under the conditions of the H1/H2-ratio of water heads above upper and lower crests less than 0.54, and a dimensionless discharge less than 2.174. The result shows that the differences between the calculated discharges by the proposed equations and the measured ones are less than 3% for flows over these CBC weirs under the present experimental conditions.     

Head-Discharge Relationships for Submerged Labyrinth Weirs

Low-head labyrinth weir control structures installed on mild sloping channels or where the channel downstream of the weir is constricting and/or heavily vegetated can experience submergence. Weir submergence occurs when the tailwater surpasses the weir crest elevation, causing an increase in the upstream driving head for a given discharge, relative to a free-discharge condition. The most familiar relationship for predicting submerged weir head-discharge relationships is likely that of James R. Villemonte, which he published in 1947 for sharp-crested linear weirs. For lack of a better alternative, Villemonte’s relation has also been applied to predicting submerged labyrinth weir performance. A new dimensionless submerged head relationship developed in this study is presented for submerged labyrinth weirs. A similar relationship is also presented for linear sharp-crested weirs. The accuracy of the submerged linear weir relationship was equivalent to Villemonte’s and is simpler to solve when working in terms of total upstream head. Relative to Villemonte’s relationship applied to labyrinth weirs, the new submerged labyrinth weir relationship reduced the predictive errors from 23 to 3.5% (maximum) and 8.9 to 0.9% (average), relative to the experimental data.     

Three-Dimensional Numerical Simulation and Analysis of Flows around a Submerged Weir in a Channel Bendway

To improve navigation conditions for barges passing through river channels, many submerged weirs (SWs) have been installed along the bendways of many waterways by the U.S. Army Corps of Engineers. This paper presents results from three-dimensional numerical simulations that were conducted to study the helical secondary current (HSC) and the near-field flow distribution around one SW. The simulated flow fields around a SW in a scale physical model were validated using experimental data. The three-dimensional flow fields around a SW, the influence of the SW on general HSC, and the implication of effectiveness of submerged weirs to realign the flow field and improve navigability in bendways were analyzed. The numerical simulations indicated that the SW significantly altered the general HSC. Its presence induced a skewed pressure difference cross its top and a triangular-shaped recirculation to the downstream side. The over-top flow tends to realign toward the inner bank and therefore improves conditions for navigation.     

Discharge Coefficient of a Triangular Side-Weir Located on a Curved Channel

This study aims to obtain sharp crested triangular side-weirs discharge coefficients both in the straight channel and along the bend by using a total of 1,735 experiments. It was found that triangular side-weirs discharging coefficients along the bend depend on the upstream Froude number in the main channel (F), the apex angle of side-weir (θ), and the bend angle (α). Because there is much greater intensity of secondary flow created by lateral flow with an increase of the overflow length, sharp crested triangular side-weirs discharge coefficients of the apex angle θ = 120° were achieved more frequently than the others even at the straight channel in subcritical flow conditions. In a curved channel, the path of maximum velocity and the secondary current created by the bend both cause a much greater deviation angle towards the side-weir which is involved within F and L/b. Therefore, triangular side-weirs discharging coefficients along the bend are greater than the values obtained in the straight channel.     

Head-Discharge Equation for Sharp-Crested Polynomial Weir

Polynomial weirs can be applied in agricultural and municipal engineering to produce a wide range of head-discharge behavior, including the proportional (linear) characteristics of the Sutro weir. This note describes a method to determine the head-discharge equations of sharp-crested weirs with openings defined by polynomials of any order n. Examples of behavior of fourth-order polynomial weirs are discussed.     

Acoustics of weirs: Potential implications for micro-hydropower noise

There is great potential for the expansion of the small or micro scale hydropower network. Of the 43 thousand weirs in the UK there are only 500 consented hydro schemes. Planning applications for such schemes require a noise assessment. Noise evaluation of a proposed renewable scheme is often complicated by the turbine sites having distinct noise characteristics in the first instance, which are often caused by the weirs themselves. Three types of weir were studied: Broad Crest weirs were studied in detail; this is complimented by further studies in Flat V and Crump weirs. Flow data was collected for ten sites from the Environment Agency and the National Rivers Flow Archive to assess the collected Sound Pressure Level (SPL) and calculated Sound poWer Level (SWL) in relation to various river flows. Weir head height, width and meteorological data were also collected. It has been shown that the SPL data collection method used was the right choice, as the greatest amplitudes at the water impact interface at all weir types was recorded. SPL and SWL were found to be within a 36–82 dBz and 45–86 dBz range respectively for all weir types. These values can be used in computer simulations of sound propagation. The mean SPL and SWL difference between the weir types are 6.1 dBz and 6.3 dBz. Head height has the greatest effect on SPLs. Attenuation with distance was found to be similar to that of a free field line source in general.     

Critical Depth Relationships in Developing Open-Channel Flow

Doubts have been expressed about the validity of the critical depth defined in terms of the minimum specific energy head of the free-surface streamline when dealing with developing open-channel flows. This note examines the two approaches for defining critical flow, that based on the minimum specific energy of the free-surface streamline and that based on the mean energy head of the whole flow section. Large differences for the dimensionless critical depths are obtained with the two methods due to each critical depth proving to be a different control point on the free-surface profile. It is argued that both methods are different alternatives, although the critical depth concept was different in each case. Theoretical support to critical flow computations based on the free streamline is provided. An alternative approach for computing the discharge characteristics of broad-crested weirs based on the energy loss inside the boundary layer is also proposed.     

Effect of Weir Face Angles on Circular-Crested Weir Flow

The standard circular-crested weir is often found in engineering applications and is used as a discharge measurement device or as an overflow structure. This research determines the discharge coefficients for ten circular-crested weir configurations with various combinations of up- and downstream angles. Two different weir heights and four different overflow depths are considered for each weir shape. For free overflow, the discharge coefficient is determined experimentally by using the total head of the approach flow. The results indicate that the upstream weir face angle has only a small effect on the discharge coefficient. In contrast, increasing the downstream weir face angle increases the discharge coefficient notably. A new formula for the discharge coefficient is presented, including both the up- and downstream weir face angles. Further, the hydraulic performance of the circular-crested weir, the resulting discharge reduction from tailwater submergence, and transition flow are discussed.