In this paper, based on the free vortex theorem and the momentum equation, a theoretical model to predict the pressure head distribution, the pressure coefficient, the end depth ratio (EDR), and flow discharge at the brink of free overfalls in channels of different cross sections with sub-critical flow is presented. Using available experimental and theoretical results of other investigators for rectangular, triangular, exponential, trapezoidal, inverted triangular ( D-shaped), inverted semicircular and also circular channels, the proposed method has been examined. The presented theory agrees well with the experiments.

Behaviour of beam depends on its depth. A beam is considered as deep, if the depth span ratio is 0.5 or more. In the available beam theories, we have to apply correction in case of deep beams. In the present work, method of initial functions (MIF) is used to study the effect of depth on the behaviour of concrete beam. The MIF is an analytical method of elasticity theory. It gives exact solutions of different types of problems without the use of assumptions about the character of stress and strain. In this method, no correction factor is required for beams having larger depth. Results are obtained for three different cases of depth span ratios and compared with available theory and finite element method-based software ANSYS. It is observed that deep beam action starts at depth span ratio equal to 0.25.

In this study, t he effect of shape of roughness elements on the bed shear stress and sequent depth of hydraulic jump have been investigated. Experiments are conducted in a rectangular flume 0f 7.5 m long and 0.3 m wide in the hydraulic laboratory of Shahid Chamran University, Ahwaz, Iran. For the purpose of this study, prismatic roughness elements with different shapes: rectangular, triangular, circular, lozenge and hexangular were tested. The roughened elements are glued on the bed of flume downstream of ogee spillway in such a way that the incoming water jet is just above the element surface. The incoming Froude number was in the range of 4.5 to 12. During each tests the water surface profile, the roller length and the jump length were measured. In few tests the longitudes and vertical flow velocity were measured. The results indicated that the presence of rough elements can reduce the sequent depth ratio.The amount of reduction would depend on the Froude number and the roughness shape. The triangular element can produce lesser sequent depth ratio.Relations have been presented in this study for the sequent depth of hydraulic jump and shear force coefficient of bed as a function of the Froude number for each roughness shape.

Since the flow at free overfall is self-calibrated, it has been extensively studied and used for flow measurement by many researchers. Previous investigations were done for different channel geometry, super and subcritical regime, with no lateral inflow along the channel, i.e. there is no variation in the discharge along the channel length. This research was conducted to investigate the discharge-end depth relationship in circular pipes carrying spatially varied flow with increasing discharge. Comparison between manometer reading and direct end depth measurements confirmed the deviation of the pressure distribution from the hydrostatic one. At the brink, nonetheless the data indicated that the end depth ratio in such flow condition is closer to unity than that of constant discharge. Consequently, based on the compiled data a relationship was proposed, which facilitates discharge. measurement with reasonable accuracy.

B-jump is defined as the jump having the toe section located on a positively sloping upstream channel and the roller end on a downstream horizontal channel. predicting the occurrence of such jump and determination of the sequent depth can help the engineer to better design the stilling basin’s wall. This is because the component of water weight within the jump can not be neglected and it is too difficult to calculate accurately. Therefore the sequent depth ratio relation can not be developed by using the momentum equation then experimental based formula should be used. In this paper first a literature reveiw is conducted then by applying the  P-theorm and defining new variable of, k, which is the upstream and downstream jump water surface elevation difference, a non dimensional relation was developed, which is not dependet on slope. To verify such relation an extensive experimental tests was conducted. By using the SPSS software an experesion was developed which show the new formula can be applied for all range of chute slope. Comparison of previous relations with our relation show that the new relation can predict the sequent depth more accurate.

One of the most important main indicators in the performance criteria of self-driving cars is the policy adopted by the self-driving system regarding the determination of vehicle speed and steering angle. To determine this policy, researchers have always faced the challenge of choosing our optimal training method between two traditional modular and modern End-to-End approaches. Recently, a lot of research has been done in order to introduce the End-to-End approach and its application in this field. In this research, an optimal model for predicting the driver's behavior has been presented using this modern approach in the form of deep learning for training artificial neural networks. In other words, achieving a model with acceptable accuracy compared to similar tasks in driving a self-driving car has been considered. For this purpose, based on the investigations carried out on the architecture of the existing networks, two architectures that have the necessary potential to achieve this goal were selected. Also, in order not to ignore the time relationship between the slides to show the visual time dependencies, and to check its effect on the result, the combination of convolutional neural networks (convolutional) with a type of recurrent network called long short-term memory LSTM was used in the training of the model. Also, a complete data set collected in real driving conditions and labeled including images and depth information has been used, and by designing training algorithms and optimizing training parameters using the Adam optimization algorithm Several trained models were presented. Among the obtained results, some predictions were more optimal than similar works, which shows the unique effect of temporal dependencies in the training and effectiveness of recurrent networks along with the strong processing of convolutional networks.

In end milling operation, cutting forces induce vibration on tool, work piece and clamping devices which affects surface integrity and quality of the product. In this process, to select the optimum end mill and machine tool, the prediction of exact cutting forces is of prime importance. In the present work, modeling and simulation of cutting forces in end milling operation are performed. Instantaneous chip geometry is predicted using a 3D simulation software, the effect of cutting depth and feed rate are calculated and cutting conditions are predicted before any machining operation.

Stilling basins are used in the outlet of channels, chutes and culverts to dissipate the excess kinetic energy of incoming flow. One of the basins in which the energy of incoming flow is dissipated by impact, is USBR VI stilling basin. The USBR VI stilling basin was first introduced by Bradely and Peterka in 1995 and then was modified by Biechley in 1978. This structure consists of a middle wall and an endsill. Scouring around the structures that are located in the vicinity of erodible beds, such as stilling basins, has always been one of the most important problems related to these structures. Unlike other types of stilling basins, the studies carried out around this type of basin are limited, and there are still many hydraulics features of this type that have not been considered in previous researches. In this article, the effect of the shape of endsill on scour depth downstream of stilling basin is evaluated. Based on Beichley graph (Standard Design), the physical model of stilling basin was designed, constructed and installed in the hydraulic laboratory of Tarbiat Modares. Experiments were conducted in a 0.8 m wide, 0.9 m height, and 0.8 m length rectangular channel. The pump used in the experiments had a nominal flow rate of 400 cubic meters per hour (about 120 liters per hour), a head of 11.7 meters, a power of 22 horsepower, and an engine speed of 1450 rpm. In the design of experiments, the parameters including approach Froude number (i.e. 1, 1.5 and 2 times of standard Froude number on Beichley graph), the diameter of inlet pipe (i.e. De = 5, 8, and 12 centimeters), and endsill shapes (triangular, stepped and circular quadrant), in the form of 27 tests were assessed to study the dimensions of the scour depth. The observations revealed that in all three endsill shapes, the increase in Froud number has led to the decrease in scour index. the circular quadrant endsill had the lowest scour depth in the front of endsill and the least scour index, in the range of the Froude number of 2 to 6. In the range of the Froude numbers of 9 to 14, the triangular endsill causes the lowest scour index. In the relative diameter of inlet pipe equals to 10.16, for Froud numbers equal to 9.27 and 13.91, the triangular shaped endsill has the least scour index. in every endsills, decreasing the pipe’s diameter results in the maximum depth of the scour. Another important finding is that sediment bar is only formed in experiments conducted with inlet pipe’s diameter equal to 5cm for Froude number equal to Froude number on Beichley graph. The biggest amounts of the height of sediment bar and maximum scour depth are found for the stepped endsill and the smallest amounts of the height of sediment bar and maximum scour depth are found for the circular quadrant endsill. Subsequently, the non-dimensional equations according to the Froud number of incoming flow and the relative diameter of inlet pipe, were presented to estimate the maximum depth of the scour hole.

Introduction: In practical applications, at the downstream of hydraulic structures, in some cases, the width of the basin may be larger than the upstream supercritical flow (sudden expansion in the flow section). In such cases, an expanding hydraulic jump with symmetrical or asymmetrical shape will be developed at the downstream. Under the design of three parallel gates, the operation of the side or middle gate can be lead to the asymmetrical or symmetrical hydraulic jump, respectively. According to the position of the jump toe, expanding hydraulic jump can be classified into four types. The present study focuses on a T-shaped hydraulic jump, which the toe is established at the beginning of the divergence section. Most of the previous studies are related to the symmetrical expanding hydraulic jump. In this case, the downstream diverging channel is symmetric on the central axis of the channel. However, a systematic study on the effects of symmetry and asymmetry of the expanding hydraulic jump was not found in the literature. In this study, using the momentum principle, some theoretical equations to determine the ratio of the sequent depths of symmetrical and asymmetrical expanding hydraulic jump were derived. Also, some regression relations were proposed to estimate the length of expanding hydraulic jump. The new proposed equations were also extended for the presence of a sill. The equations were calibrated using available experimental data obtained in this and previous studies. This research also considered the characteristics of expanding hydraulic jump under the symmetrical and asymmetrical operation of the parallel gates. Methodology: To calibrate new proposed relations and investigate the effects of different parameters on the expanding hydraulic jump characteristics, two experimental data sets were used. In addition to the data set from Bremen (1990), the experimental data from the present study were used. The data were collected from a hydraulic model of three parallel radial gates for operating the side or middle gate, which corresponds with the asymmetrical or symmetrical expanding hydraulic jump, respectively. The experiments provided a wide range of different parameters as the approaching Froude number, hydraulic jump length, sequent depths ratio, divergence ratio, sill height, and relative length of gate separator wall. Results and discussion: Equation (4) was developed to determine the ratio of the sequent depths of expanding hydraulic jump based on the momentum equation. For the presence of a sill, a combination of Equations (4), (7) and (8) can be used to calculate the ratio of the sequent depths under the asymmetric and symmetric developments, respectively. Determining the ratio of the sequent depths requires the calculation of the adjacent water depths of the closed gates. For this purpose, in addition to regression equation development (i. e. Equation 13), Equation (12) was proposed. This equation is based on the calculation of the hydraulic jump profile. It was observed that under the calibration range, the regression equation is more accurate. However, Equation (12) is recommended for the range outside of the experimental observations. The results showed that: ❖ As the divergence ratio increases, the ratio of sequent depths approaches to the classic hydraulic jump. ❖ By decreasing the relative length of the gate separator wall and decreasing the width of the gate on the downstream channel width, the relative depth at the side gate and consequently the ratio of the sequent depths will decrease. ❖ For the lower length of the separator wall and under the operation of the middle gate, longer horizonta distance is needed to develop the jump than the side gate. However, as the length of the separator wall increases, the length and sequent depth of hydraulic jump due to the side gate increases on the middle gate. ❖ In the presence of a sill, the relative length of the hydraulic jump decreases, and the ratio of secondary depths increases. ❖ It was observed that the hydraulic jump due to the operation of the middle gate leans toward the left or right side of the channel due to oscillatory behavior. ❖ Under operating the middle gate and in the absence of a sill, an asymmetric hydraulic jump is formed in the channel face when the length of the separator wall is less than 38% of the classical hydraulic jump length. For the presence of a sill, the minimum length of the separator wall decreases to about 26%. ❖ By decreasing the initial depth of the hydraulic jump on the width of the gate and converting the output jet into a linear jet, the relative development length will be increased. ❖ As the sill height increases, the difference in the depths attached to the side gates will decrease, and the hydraulic jump will develop more symmetrically. ❖ As the relative height of the sill decreases, the minimum length of the separator wall increases and a symmetrical hydraulic jump in the flanks forms. Conclusion: This research developed a set of theoretical and regression relationships for estimating the length and sequent depth ratio of expanding hydraulic jump. Moreover, the effects of sill height, divergence ratio, and the length of the gate separator wall, were investigated. This study compares the effects of side and middle gate operations based on the variation of jump length and sequent depth ratio. The results can be used as a guide for the hydraulic structures operators to reduce the asymmetric severity of the expanding hydraulic jump and achieving the complete development under the minimum length.