Novel Approach to Computing Critical and Normal Depth in Circular Channels

The critical depth and normal depth computation are essential for hydraulic engineers to understanding the characteristics of varied flow in open channels. These depths are fundamental to analyze the flow for irrigation, drainage, and sewer pipes. Several explicit solutions to calculate critical and normal depths in different shape open channels were discovered over time. Regardless of the complexity of using these explicit solutions, these formulas have a significant error percentage compared to the exact solution. Therefore, this research explicitly calculates the normal and critical depth in circular channels and finds simple, fast, and accurate equations. First, the dimensional analysis was used to propose an analytical equation for measuring the circular channels' critical and normal depths. Then, regression analysis has been carried for 2160 sets of discharge versus critical and normal depths data in a circular open channel. The results show that this study's proposed equation for measuring the circular channels' critical and normal depths overcomes the error percentage in previous studies. Furthermore, the proposed equation offers efficiency and precision compared with other previous solutions.

Experimental determination of the critical depth of cutting of blocked soil cutting by cutters and the length of the ploughshare of chain excavators

The development of civil and industrial construction and the growing trend of construction of underground communications have led to an increase in the volume of work on the laying of gas and oil pipelines, water mains, sewerage systems, power cables and communication cables. Much of the excavation work in the construction of these communications is performed by trench excavators.

Determination of kinematic and geometric parameters of multi-scraper chain trange excavators on the basis of the semi-blocked critical depth regime of soil cutting

Trench excavators with a chain-scraper working body became widespread in the construction of linearly extended objects. Increasing workloads and rising energy prices call for optimizing the parameters of construction machinery. The most important component of the process of digging the soil with a chain-scraper working body is cutting the soil with scrapers (knives).When calculating the cutting forces, the working body is taken as a complex mechanical system of traction chains and transverse beams, on which in a certain order are arranged and fixed scrapers-knives with known angular parameters. Separation of chips from the soil is carried out by each scraper in the conditions of blocked, semi-blocked and free cutting of the soil. It should also be borne in mind the change in resistivity and energy consumption of soil cutting with a change in chip thickness. The minimum energy consumption of soil destruction takes place at a critical depth of cut. To reduce the energy consumption of the soil destruction process, a method of calculating the parameters of chain-scraper working bodies of trench excavators is proposed, which is based on critical depth cutting of soils. The initial data for the calculation are: technical productivity, m3 / h; maximum trench depth, m; trench width, m; physical and mechanical characteristics of soils (coefficient of adhesion, specific gravity, angles of internal and external friction). The proposed calculation method allows to determine the technological and geometric parameters of the chain-scraper working body with critical depth cutting of soils.

A SIMPLE APPROACH TO THE STUDY OF WAVE PATTERNS

The paper revisits some pioneering work of Sir Thomas Havelock on wave patterns with particular attention focussed on his graphical method of analysis. Motivated by a desire to explore this method further using numerical methods, it is extended in a simple manner to give three-dimensional illustrations of the wave patterns of a point disturbance in deep and shallow water. All results are confined to the sub- and trans-critical regimes with some obtained very close to the critical Depth Froude Number. Some conclusions are drawn on the wave types produced when operating close to the critical speed and their decay with distance off.

WEB INTERFACE FOR DETERMINING CRITICAL DEPTH IN OPEN CHANNEL

Research and calculations of non-uniform motion are very important from a practical point of view and have certain features for different states of flow, analysis of the shape of free surface curves, as well as the design of many hydraulic structures. When considering these issues, the concepts of specific cross-sectional energy and critical depth are used. The current trend of technology development in the educational process is based on Internet communications, instant online calculations and mobile microprocessor gadgets with appropriate software. The presented experimental project of educational and methodical material with web forms of online calculation of individual tasks is a variant of the modern competitive online environment on the Internet. Further direction of development - addition of methodical video, audio and graphic elements. Analysis of web analytics will gradually simplify the interface and choose the most effective set of modern formats for teaching materials. Computer on-line calculations allow to change the initial data and to introduce elements of modeling and in-depth study of theoretical positions using one typical example in the form of a web form

A Novel Methodology to Investigate Critical Depth for Ductile-to-Brittle Transition During Scratch Testing

More than two decades have passed since the introduction of the scratch testing method for rock strength determination. The test method typically involves dragging a rigid-shaped cutter across the rock surface at a fixed cutting depth. This depth determines the failure mechanism of the rock, ductile for shallow depths and brittle for deeper. In the ductile mode, intrinsic specific energy is primarily a measure of the unconfined-compressive-strength (UCS), which is pivotal for rate of penetration (ROP) during drilling and for borehole stability analysis. On the contrary, brittle failure can lead to permanent core damage and is usually not desired as it impacts interpretation of the scratch testing results. Consequently, it is imperative to identify the critical depth, and at which transition from ductile to brittle failure occurs which will help optimize rock testing and tool designs. In this study, a novel methodology is proposed utilizing micro-computed tomography (CT) imaging to determine critical depth through morphological analysis of scratch test cuttings. Scratch tests are carried out on Indiana limestone core samples with the cutter-rock interaction geometry characterized by a cutter width of 10mm and a back-rake angle of 15°. The sample is scratched in the range of 0.05mm to 0.40mm with increments of 0.05mm. Scratch powder is carefully collected after each scratch increment and stored for further analysis. This powder is then loaded into slim rubber tubes and imaged at a high resolution of 1 µm with a helical micro-CT scanner. The scans are then reconstructed using a computer program to initiate the visualization of individual grains from each cutter depth including evaluation of grain morphologies. Finally, the results from this morphological analysis are corroborated and compared with three other methods: force response analysis, force inflection point analysis, and the size effect law (SEL). Based on shape analysis, it was found that the transition from ductile to brittle regime occurs at a depth of 0.25mm. Elongation and appearance of the enhanced degree of angularity of the grains as the depth of cut (DOC) increases past 0.25mm was observed. Moreover, large grain sizes were detected and are representative of formation of chips (typical brittle regime response). Furthermore, it is illustrated that the image analysis helps eliminate the ambiguity of force signal analysis and in combination can aid in the critical depth of cut determination. The other methods involving force alone and the SEL are not able to pin-point onset of brittle regime. Using a similar methodology, creation of a database for various rock types is recommended to develop a guide for the depth of cut selection during scratch testing. This novel methodology utilizing micro-CT analysis and comparative study with other techniques will put in place an accurate strategy to determine the critical depth of cut when designing rock scratch testing programs.

Analysis of the possibility of a submarine implosion using finite element method

Recently, there have been reports of disasters related to the disappearance of submarines. One of the potential causes of disasters is the ship’s descent to the so-called critical depth and its subsequent implosion. However, the occurrence of the submarine implosion phenomenon may be difficult to achieve. This is due to the presence of hydraulic fittings and other more susceptible hull components. The article presents an analysis of the strength of a fragment of the submarine’s hull, modelled on Kobben-class ships, to demonstrate the possibility of an implosion. Furthermore, the construction of submarines was presented, and phenomena related to the strength of submarine hulls using FEM were discussed.

Estimating output flow depth from Rockfill Porous media

To analyze the flow in a rockfill porous media using the Gradually Varied Flows theory (one-dimensional flow analysis) and solving the Parkin equation (two-dimensional flow analysis), calculation of the output flow depth as the downstream boundary condition is of great importance. In most previous studies, the output flow depth has been considered equal to the critical depth. In the rockfill porous media, unlike free surface channels, the fluid weight is exerted to the aggregates in addition to the flow, and therefore, the output flow depth from the rockfill is always greater than the critical depth (flow leaves the rockfill with a specific energy greater than the critical energy), and is expressed as a coefficient (Γ) of the critical depth. In the present study, using dimensional analysis and particle swarm optimization (PSO) algorithm and experimental data in different conditions (a total of 178 experimental data for rounded, crashed, Glass artificial materials with rhomboid structure, Glass artificial materials with cubic structure, sandy natural materials), an equation was presented to calculate the mentioned coefficient as a function of the physical characteristics of the rockfill porous media as well as the flow that can be used for all experimental conditions with high accuracy. If the output flow depth is considered to be equal to the critical depth, the mean relative error (MRE) in terms of using the experimental data of the mentioned materials separately and for the data of all the mentioned materials together was equal to 84.40, 83.81, 60.62, 67.68, 74.82 and 69.96%, respectively. In the case of using the proposed equation in the present study, the corresponding values of 5.49, 4.72, 6.24, 4.41, 6.42 and 8.99% were calculated, respectively.

Laboratory Investigation of Hydraulic Parameters on Inclined Drop Equipped with Fishway Elements

This study aims to provide a way to increase the energy dissipation of flow in the inclined drop with environmental and economic considerations. Eighty-one experiments were performed on three types of simple inclined drop and inclined drop equipped with hole and without hole fishway elements with a 200~600 L/min flow rate. In this study, the effect of using fishway elements on hydraulic parameters regarding flow pattern, energy dissipation, relative downstream depth, relative aeration length, relative length of the hydraulic jump, and downstream Froude number of an inclined drop was investigated through physical modeling following the symmetry law. The results showed that in all experimental models, with increasing the relative critical depth parameter, the energy dissipation values increase, and the downstream Froude number decreases. The parameters of relative downstream depth, relative length of a hydraulic jump, and relative aeration length also increase with increasing relative critical depth. On average, 88% of the flow energy dissipation increases with the design of the fishway elements on the structure compared to the simple drop. Model M7 (with holes fish elements) shows the highest energy dissipation, and Model M2 (without holes fish elements) has the highest flow aeration length and relative downstream water depth.