Part I presents the statistical theory of turbulence, and Part 2 the coherent structures in open-channel flows and boundary layers. The book is intended for advanced students and researchers in hydraulic research, fluid mechanics, environmental sciences and related disciplines. References Index.

Turbulence in open-channel flows

Piano Key Weirs (PKWs) are an alternative to linear overflow structures, increasing the unit discharge for similar heads and spillway widths. Thus, they allow to operate reservoirs with elevated supply levels, thereby providing additional storage volume. As they are relatively novel structures, few design criteria are available. Hence, physical model tests of prototypes are required. This study describes comprehensive model tests on a sectional set-up of several A-type PKWs, in which the relevant parameters were systematically varied. Considering data of former studies, a general design equation relating to the head–discharge ratio is derived and discussed. The latter is mainly a function of the approach flow head, the developed crest length, the inlet key height, and the transverse width. To extend its application range, case study model tests were analysed to provide a design approach if reservoir approach flow instead of channel flow is considered.

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Hydraulic design of A-type Piano Key Weirs

Piano Key Weirs are an effective solution for dam rehabilitation as well as new dam projects with a high level of hydraulic constraints. In order to improve the efficiency of their design, an experimental study of the influence of the main geometric parameters has been performed. Thirty one configurations were tested for a wide range of discharges. The results of the study show the influence of the weir height, the keys widths and the overhangs lengths on the discharge capacity and flow characteristics. Based on hydraulic considerations, optimum values of the main geometric ratios are provided. An analytical formulation is developed to predict the discharge capacity of the weir as a function of its geometry. It shows an accuracy of 10% compared to the experimental results of this study and from other sources.

Experimental parametric study and design of Piano Key Weirs

With inertia and gravity representing the dominant forces for most open channel flow applications (e.g. weir flow), Froude similitude is commonly used for scaling hydraulic performance data from the model to prototype structures. With weir flow, as the upstream head decreases, however, the relevance of surface tension and viscosity forces can increase to the point when the model and prototype similitude is not fully achieved through Froude scaling. Such discrepancies are referred as size-scale effects, and among other things, can result in variations in the head–discharge relationship, nappe trajectory, and air entrainment. Published criteria for avoiding significant size-scale effects for free flow over linear weirs have suggested that minimal heads of ∼0.02 to 0.07 m be respected, independently of the model size. In this study, the size-scale effect, minimum upstream head, and Weber number limits are investigated for four piano key weirs with geometric model scales of 1:1, 1:7, 1:15, and 1:25.

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Scale effects in physical piano key weirs models

A piano key (PK) weir is a type of nonlinear (labyrinth-type) control structure with a relatively small spillway footprint. No standard PK weir design procedure is available, and the amount...

Piano Key Weir Hydraulics and Labyrinth Weir Comparison

In recent years, spillway rehabilitation has increased in importance and become the subject of many projects worldwide. One solution for this problem is the implementation of a new type of labyrinth spillway, called Piano Key Weir (PK-Weir ). This is an excellent alternative for increasing the overflow capacity of existing dams. Similarly to traditional labyrinth weirs, the hydraulic capacity of a PK-Weir is a function of its geometrical characteristics. Currently, there is a lack of systematic experiments, and the existing data does not allow the proposition of a universal design procedure. This paper reviews the previous studies on the efficiency of planned and built PK-Weirs. The results are evaluated by comparing an actual PK-Weir’s discharge to that theoretically obtained for a sharp-crested spillway with crest length equal to the width of the PK-Weir for a given hydraulic head. On the basis of this evaluation, a preliminary design procedure is proposed.

Discharge Capacity of Piano Key Weirs

Sediment particles entrainment from the channel bed is influenced by flow turbulence which creates fluctuating shear stress at the bed. Sweep quadrant event is considered to be most important for entrainment of sediment particles as it exerts forces in the flow direction resulting in rolling and sliding of sediment particle. Similarly, the ejection event has been considered important for sediment transport since these events maintain the sediment particles in suspension. In this paper, the nature of bursting events and in particular, the sweep events were studied in a model of braided river with a central island. The instantaneous velocities of flow were measured using the ADV. The turbulent stresses were determined from these instantaneous velocities. Box–Cox transformation is applied to transform the original data into a normally distributed data. The velocity measurements near the braided bar were made at 12 vertical sections using an ADV. The maximum value of turbulent kinetic energy and the R...

Experimental study on bursting events around a bar in physical model of a braided channel

Development of irrigation schedules that lead to efficient use of water is imperative. For this, crop experiments were conducted in the humid sub-tropical climate region of Western Uttar Pradesh, India, where a plant-based index, crop water stress index (CWSI), has been derived for a crop season of wheat crop. Four irrigation treatments, two equipped with drip irrigation and two with flood irrigation, of 25% MAD (drip), 50% MAD (drip), 50% MAD (flood), and a farmer’s field replication (flood) were experimented in the study. MAD is maximum allowable deficit that represents the soil moisture depletion at which irrigation was applied. Research-grade infrared thermometers were used for field measurements of crop canopy temperature. The empirical approach of CWSI is applied to formulate lower and upper baselines utilizing the air temperature humidity parameters and CWSI values for wheat crop for the pre-heading and post-heading stages are derived. Mean CWSI values for irrigation treatments are found out as 0.03, 0.11, 0.29, and 0.31 for 25% MAD (drip), 50% (drip), 50% (flood), and a farmer’s field replication (flood), respectively, during the crop period with the higher values of CWSI representing more crop water stress. The highest water use efficiency (WUE) of 26.9 kg/ha-mm is observed for 50% MAD (drip) irrigation treatment with a mean CWSI value of 0.11. The farmer’s field replication, which corresponds to the lowest WUE, has by far the highest value of mean CWSI during the post-heading stage. The use of a plant-based index rather than the conventional soil moisture method can be a more effective method to determine water-efficient irrigation schedules. 

Crop Water Stress Index for Devising Water Efficient Irrigation Schedules for Wheat Crop

In view of the growing water scarcity, particularly in the backdrop of climate change the adoption of waterefficient irrigation systems is becoming indispensable. The study of efficient irrigation systems is lacking in the developing countries like India, which is in turn responsible for the low values of water-use efficiency in agriculture. Therefore in this article, different irrigation systems studied for the developing countries, including the water-efficient and traditional ones, are reappraised. The irrigation systems are assessed on the basis of various factors such as economic parameters, water productivity, water saving and crop yield. Among water-efficient irrigation systems, drip irrigation system (DS) is considered to be the most successful method for water conservation and increased agricultural output. DS not only reduces the cost of supplied water, but also those incurred in the activities such as human labour and other cultivation costs. DS is found suitable for a variety of crops, including cereals, vegetables and cash crops in different regions of the world. Water saving and electricity saving is in the range 40– 54% and 26–47% respectively, when DS is compared with the surface irrigation methods. For most of the crops, drip irrigation is found to be the most robust, profitable and cost-effective method of irrigation and could be a possible solution to the growing water shortage in the backdrop of climate change.

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Techno-economic analysis of irrigation systems for efficient water use in the backdrop of climate change

Bridges overhead rivers require exceptional safety and channel rehabilitation due to the erosive impact of water. There has been a lot of research into designing efficient countermeasures for scour protection and treatment of channel instability near bridges. Interestingly, most of these studies use flow-modifying structures to regulate flow and sediment migration on the upstream side of bridges. Notably, the flow-modifying structures are proven to be effective tools in bridge pier protection since their working premise is the counteracting of vortices or realignment of flow. Hence, to develop proper knowledge, this paper focuses on flow deflecting structures with the aim of modifying flow by realignment. The study begins with an evaluation of several hydraulic challenges associated with modern bridges worldwide. Thereafter, the literature featuring flow deflecting devices, such as submerged vanes, rock vanes, cross vanes, and w-weirs, is discussed. In doing so, the fundamentals of how these devices restore the flow by keeping the maximum scour depth away from the bridge abutment and pier are addressed. Further, the capabilities of the flow deflecting devices on smooth and safe flow transfer through bridge openings are highlighted. In addition, a thorough examination of bridge safety during pressure flow is included in the study. 

Gopal Das Singhal

Papers

Discharge Capacity of Piano Key Weirs

Experimental study on bursting events around a bar in physical model of a braided channel

Crop Water Stress Index for Devising Water Efficient Irrigation Schedules for Wheat Crop

Techno-economic analysis of irrigation systems for efficient water use in the backdrop of climate change

A review of bridge scour mitigation measures using flow deflecting structures