| Abstract: |
. Statistical models were developed and their results were pared to the experimental ones.In the theoretical study, prediction theoretical models were developed to pute the relative depth of jump and the relative energy lossExperimental and theoretical studies were carried out to investigate the merged tlow characteristics downstream of a control gate in a non-prismatic el reach. The sides of the channel are gradually diverging tlu’ough a length 130 cm and a fixed divergence angle of 5.280 was used. This non-prismatic el reach may contain an end sill or may contain a negative step or both end and negative step. Through the course of the study, the type of non-prismatic mel reach is termed radial stilling basin provided with end sill, or negative p or both end sill and negative step. Different heights of the ES were tested d different positions of NE were also considered. All considered models were ed under a considerable range of submergence ratios. The experiments ¥ered wide ranges of the parameters as follows: 2SF1S7, 3.5SSS10, oS3.5, ro= 1.4-1.67, and r=(1-1.5). All the experimental results were analyzed discussed, too. The retically derived equations were verified using the experimental data. The d of applying a correction factor to the theoretical models was investigated.The basics of the artificial neural network (ANN) were introduced. The was applied to develop a prediction ANN model to predict the basicacteristics of the submerged hydraulic jump. The results of the developed models were compared to those of the developed statistical and theoreticalThe main conclusions of the present research may be summarized in the !lowing ones.1- Theoretical Models are developed llsmg the I-D flow equations to compute the relative depth (Eqns. (3.6) and (3.16)) and the relative energy loss (Eqns. (3.10) and (3.20)) of the submerged hydraulic jump fonned in radial basin provided with negative step and lor end sill.2- The dimensional analysis is used to obtain the functional relationship between the length of jump (Also for Yo and Et/Ej) and the relevant factors such as Froude number, submergence, the relative height of the step, the relative position of the step and the relative height of the sill Eqns. (3.25) to (3.27).3- Statistical models are developed using the experimental data and based on the functional relationship derived from dimensional analysis to compute the relative length of jump (Also for Yo and EdE1) for all tested basins (Eqns. (7.1), (7.2), (7.4), (7.5), (8.5), (8.6) and (8.7).4- Neural network models are developed for all tested basins to predict the main characteristics of the hydraulic jump (relative depth, relative energy loss and relative length of jump).5- The developed theoretical models are verified llsing the experimental data. Good agreement is obtained for each model.6- The need for a correction factor to account for the simplified assumptions is investigated and it is found that the accuracy of the theoretical models is practically accepted because the resulting errors are less than 5% in most of the cases.ly, The developed equations based on the dimensional analysis for the length of jmnp agreed well with the experimental results for all tested basins.The predictions of the neural network models are much better than the empirically developed models and are comparable with the theoretically developed models.Theoretically and experimental the relative depth increases with the increase of the submergence ratio while the relative energy loss decreases with the increase of the submergence ratio.Theoretically and experimentally, both the relative depth and the relative energy loss increase with the increase of the Froude number.Theoretically and experimentally, the presence of the negative step in the radial basin increases the relative depth of the jmnp and the rate of increase increases as the steps moves downstream from the begilming of the basin towards the end of the basin.Theoretically and experimentally, the presence of the negative step in the radial basin decreases the relative energy loss and the rate of decrease increases as the steps moves downstream from the beginning of the basin towards the end of the basin.Experimentally the presence of the negative step 111 the radial basin increases the relative length of the jump as the steps moves downstream from the beginning of the basin towards the end of the basin.14- Theoretically and experimentally, the presence of end sill reduces the relative depth of jump and increases the relative energy loss. However, the effect of end sill is small and practically can be neglected.15- Experimentally the presence of end sill reduces the relative length of jump, the effect of end sill is small and practically can be neglected.16- The theoretical models for the cases where no end sill exists can be used safely to compute the relative depth and the relative energy loss of the jump Eqns. (3.7 and 3.11), in cases of small relative sill height.17- The neural network models are promising in the field of the Hydraulic Engineering and especially in the field of hydraulic j mnp: present study is highly recommended the following fmiher studies for Ire investigations:1- The effect of step height on the submerged hydraulic Jump characteristics needs more investigations.2- The effect of the positive step in radial basin on the submerged hydraulic jump characteristics needs to be investigated.3- The effects of both negative and positive steps on the characteristics of free radial hydraulic jump are not yet investigated.4- The effects of multi-steps on both free and submerged hydraulic jumps in radial basins are not yet investigated.5- Velocity distribution and pressure distribution in the vicinity of the steps under radial il-ee and raclial submerged hydraulic jumps are not yet investigated.6- The effect of entrained aIr on both free and hydraulic jump characteristics fonned in radial basins with steps is not yet investigated 7- Carrying out this research using movable soil bed 8- Applying this study on regulators having tow or mor vents.
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