Crest Length Research Articles

Energy dissipation performance of labyrinth and harmonic stepped spillways

ABSTRACT Stepped spillways are structures that dissipate the energy on steps, especially in topography, where building the energy dissipate pool is impossible as long as required. For this reason, stepped spillways are one of the critical topics that have attracted the attention of researchers for many years. It has been the subject of many studies, especially because the step geometry is an effective parameter in the energy dissipation rate. In this study, the effect of the labyrinth and harmonic geometry on the plan on energy dissipation performance is examined using the open-source OpenFOAM software. The 11 different geometries were analyzed in detail and discussed with the literature results. For analysis, the k − ω SST turbulence model and the multi-phase solver interFoam were utilized. The results showed that the number of cycles is an effective parameter for energy dissipation performance; the energy dissipation rate increases when effective crest length increases, and labyrinth and harmonic models could dissipate about 20% more energy than the flat model.

Characteristics and migration of subaqueous sand dunes influenced by internal solitary waves in the Dongsha Region, Northern South China Sea

Seabed data acquired from the Dongsha Region in the northern South China Sea (SCS) revealed the detailed morphology of sand dune fields on the upper continental slope, at depths between 230 and 1240 m. High-resolution multibeam echosounder bathymetry and multichannel seismic reflection data were used to describe and interpret the distribution, characteristics, and migration of these sand dunes. The sand dunes were distributed as patches on a generally gentle continental slope (gradients≤0.58°), on a seafloor mainly covered by silty and coarse sand. The dunes exhibited distinctly different distribution patterns, geometries, and migration behavior. The trough-to-trough wavelength ranged from 47 to 555 m, the height was 0.1 to 19.8 m, the crest length was 100 m to 10s of km, and the dominant orientation was NE-SW. Based on their distribution and characteristics, the sand dunes were further categorized into (i) sinuous, (ii) barchan, (iii) reticular, (iv) restricted, and (v) superimposed types. Most sand dunes migrated to both NW and SE directions. We infer that, in the Dongsha Region, northern SCS, sand dunes formed and migrated due the world's largest observed internal solitary waves (ISWs). Wave-wave and wave-topography interactions occur as ISWs propagate and undergo polarity conversion during shoaling process, reflection, refraction, diffraction at the Dongsha Atoll. These processes bring about variable and complex local hydrodynamic conditions in the Dongsha Region, dissipate vast amounts of energy, erode the seafloor, and supply the sediment and energy required to sustain the formation and migration of very large sand dunes. Our findings not only enhance our understanding of the intricate relationships between topographic and geomorphologic evolution, sedimentary dynamics and mesoscale motions, but also hold significant importance for various hydrographic applications, such as navigation and submarine pipeline installation.

An experimental and numerical investigation of hydraulic performance of in-channel triangular labyrinth weir for free overflow

ABSTRACT Labyrinth weirs are well known for their superiority in providing higher flow capacity for a given hydraulic head, especially in areas where space is limited. This study presents an experimental and numerical study to determine the hydraulic efficiency of triangular labyrinth weirs. The discharge coefficient of a weir was determined in two different ways, depending on the width of the channel (C d ) and the length of the crest of the weir (C L ). Although the crest length is the most important factor in increasing the discharge coefficient per unit channel width, the discharge coefficient per unit crest length decreases with increasing the crest length for a given head. It can be said that the main reason for the reduction in weir efficiency, particularly at high headwater, is nappe interference and therefore local submergence between cycles. From the results of systematic analyses, some new highly correlated multiple regression equations calculating these two coefficients in relation to the weir geometries and the flow conditions were obtained. As a result of the literature comparison, although they were found to be generally compatible with the results of similar studies in the literature, the reasons for the differences between them were discussed.

Characteristics of internal waves in the Bali Sea from Sentinel-1A data and ocean modeling

Abstract Internal waves (IWs) that propagate into the Bali Sea are supposed to originate from the generating sill area in the southern part of the Lombok Strait. This study aims to investigate surface features and mechanism of IWs formation and propagation into the Bali Sea. The datasets are acquired from the Sentinel-1A imageries and CROCO model simulation. The results showed that solitary wave packets are spread over two areas: near Lombok Strait as generating area, and in the western and northern parts of the Bali Sea as propagating area. The length of IWs crests increased as they moved into the propagation area. The model showed that mixed semidiurnal tidal currents near the sill flow northward (southward) alternately during the flood (ebb) tidal period, resulting in the pycnocline deepening down to ~400 m near the northern sill area during the flood tide. Furthermore, the model demonstrated an alternating upward and downward movement of vertical currents components, associated with propagation of IWs’ crests and troughs along IWs pathway.

Experimental and numerical investigation of rectangular labyrinth weirs in an open channel

Labyrinth weirs are commonly used to increase the discharge efficiency in free-overflow discharges. These weirs provide a higher discharge efficiency than conventional linear weirs at the same headwater. In this study, the hydraulic performance of rectangular labyrinth weirs (RLWs) under different geometries and flow conditions was investigated experimentally and numerically. The numerical model was verified and validated using the grid convergence index method and experimental data. Numerical modelling results showed increased performance of the RLW due to the distribution of lateral velocities in the inlet keys, while nappe interference in the downstream keys led to a decrease in performance at high headwater. Within the limitations of 1.5 ≤ L/B ≤ 2.33 and 0.1 < Ho/P < 0.61 (L is the weir crest length, B is the channel width, Ho is the total water head and P is the weir height), a performance increase of 44% on average (maximum increase of 67%) for unit channel width was found for RLWs compared with linear weirs. For these limitations, two new empirical formulas with a high correlation were derived to estimate the discharge coefficients of RLWs based on B and L for Ho/P > 0.1, which are widely used in practice. When compared with some data in the literature, the empirical formulas produced satisfactory results.

Internal solitary waves observation and feature extraction based on wavelet transform by Sentinel-1A in Lombok Strait, Indonesia

Lombok Strait is an essential pathway in trans-oceanic water mass transport. Due to this water mass transport flowing over Indonesian waters, the current is known as Indonesian Throughflow (ITF), which plays a role in the transfer of warm water masses from the Pacific to the Indian Ocean annually. Lombok Strait has intensive characteristics of the internal waves (IWs) generation because of the strong current that passes through the complex bathymetry along the strait area. IWs with large amplitude and nonlinear properties are known as Internal Solitary Waves (ISW) that can be detected by Synthetic Aperture Radar (SAR) images. A Wavelet Transform method for ISW feature extraction was applied to SAR images by Sentinel-1A (C-band). ISW packet characteristics can be distinguished from other phenomena based on their geometrical structure and shape. ISW packet pattern consists of light and dark lines which decrease intensity from front to rear. SAR observation detected 5 parameters (phase speed, soliton numbers, wavelength, first crest length, and propagation direction). The arc-like ISW in the Lombok Strait propagated to the North of the sill with average phase speeds of about 2.13 m/s and was frequently detected during the northwest monsoon (NWM). The detected soliton number is less than 6 solitons per packet with a wavelength of about 1 – 4 km, and the first crest length varies from about 12.16 km to more than 100 km. ISW detected in Sentinel-1A images were located at the bathymetry about 800 meters around the Lombok Strait area.

Parametric study of flow at circular piano-key inlets over the vertical shaft spillways

Swirling flow at vertical shaft spillways results in flow fluctuations, reduces hydraulic system efficiency, and causes structural damage. Optimizing the shape of the inlet is a practical means to decrease the swirling flow strength. In the present study a comprehensive experimental investigation was performed to examine the effects of a new type of inlet over vertical shaft spillways, namely the circular piano-key (CPK) inlet, for free, orifice and full-pipe or black water flow regimes. Head-discharge relationships, threshold and critical submergence depths and the effects of different geometrical parameters of the CPK inlets on the spillway flow discharge coefficient were assessed. Results reveal that increases in the height of the inlet and outlet keys increase the released capacity of the shaft spillway. Given its increased total crest length and the effects of the radially placed walls of a CPK against the swirling flow, angles of the inlet and outlet keys of the CPK are found to significantly affect the spillway flow discharge. The effect of inlet and outlet overhangs on the efficiency of CPK inlets is not noteworthy, being negligible. Considering the destructive effects of swirling flow, the CPK inlets significantly decrease the range of submergence for an unfavourable swirling flow regime condition, increasing the threshold submergence depth and decreasing the critical submergence depth. The flow discharge through the CPK inlets is higher than those of the other circular-type spillways. The present modified CPK inlets more effectively divert water, serving as an economical alternative to the conventional circular spillways.

Flow discharge coefficient of crest weirs with covered vegetation

The flow data of mountainous rivers is very important in hydrological forecasting. Crest weirs with smooth surface have been widely used and studied, while there is little information on the weir covered with vegetation. In this experiment, the flow coefficient reduction are systematically investigated by different density flexible artificial vegetation, in addition to the changes of discharge, crest length and height. The equivalent roughness height of vegetation on the weir was calculated. It was found that the flow coefficient with vegetation is smaller than smooth crest. According to the ratio of upstream water head to the length of vegetation weir crest, the experimental flow can be divided into broad-crested weir flow rate of H/L < 0.4 and narrow-crested weir flow rate of H/L > 0.4. The flow coefficient reduction rate of both types of weir flow rates varies to a certain extent. Experimental data showed that the crest weir height H/P played a different law for the broad-crested weir and narrow-crested weir. Taking into account the influence of vegetation, crest length and height, empirical formula for flow coefficient was proposed for flow estimation correction.

A performance comparison of the meta model methods for discharge coefficient prediction of labyrinth weirs

Weirs are hydraulic structures with various applications, such as flow measurement, flow diverting, and/or flow control. Labyrinth weir as a nonlinear weir with a folded crest enhances the spillway system discharge capacity by increasing the crest length for a given channel width. As a remarkable parameter, the discharge coefficient plays an important role in determining weirs' passing capacity. So, it is important that the discharge coefficient be accurately represented to ensure an appropriate and economical design. This research evaluates the prediction accuracy of four soft computing techniques, such as support vector machines (SVM), gene expression programming (GEP), software (QNET), and artificial intelligence networks (ANN), to predict the discharge coefficient of labyrinth weirs using three different scenarios. The model's input parameters included the total water head ratio (HT/P), magnification (Lc/W), and cycle wall angle (α). On reviewing the outcomes of the developed models, it appeared that each of them demonstrated satisfactory performance in predicting the discharge coefficient. However, ANN and SVM reveal more accuracy compared to other techniques. The prediction results reveal that the ANN as a superior model has the following performance metrics: R2 = 0.998, DC coefficient = 0.996, and RMSE = 0.006. The sensitivity analysis results indicate that HT/P is the most effective factor in determining the labyrinth weir discharge coefficient in all methods. This suggests that the ratio of HT (total water head) to P (weir height) has a significant impact on the overall model performance. Upon comparing the results of this research with those of other researchers, it is evident that the evaluation indicators for all methods employed in this study are relatively superior.

Numerical study on discharge capacity of piano key side weir with various ratios of the crest length to the width

Abstract A side or lateral weir can be defined as a longitudinal weir put in parallel to the main flow direction. A piano key side weir (PKSW) is one of the various side weirs used to control flow level, flow diversion, and flood harm prevention in dams and hydraulic systems. A side weir aims to keep the water level in the main channel at a specific level by discharging the overflow water into a side channel. The discharge coefficient of the PKSW was covered in this study by numerical modeling of a rectangular PKSW type B with various ratios of the crest length to the width in a straight channel. Results showed that the discharge coefficient of the PKSW was more affected by the L/W parameter when the other parameters were constant. It was noted that the PKSW discharge coefficient for L/W equal to 6 demonstrated a significantly higher level of performance and also found that increasing the upstream head above the side weir crest (h a/P) negatively affected the coefficient of discharge. It was concluded that a high capacity of the discharge coefficient required the (h a/P) ratio to be smaller than 0.75 or within the range (0.3 ≤ h a/P &lt; 0.75).

Flow behavior over well-escape weirs

ABSTRACT Weirs play an important role in controlling and managing water in irrigation canal networks through several functions, such as discharge measurements, water distribution, and lowering the water level. Weirs also play a crucial role in protecting canals from flooding, which might cause the earthen banks to collapse, by eliminating surplus water at the ends of the canals. Over the previous decades, the flow over the traditional sharp-crested weirs was extensively investigated by many researchers; however, the well-escape weirs have not received sufficient attention. These types of weirs were mostly constructed in the form of vertical wells that may be circular or rectangular in shape, and water may flow through the entire perimeter of the weir or part of the perimeter. In the present research, the effect of the well-escape-weir shape on the characteristics of flow over the weir was studied. A set of models were constructed in different shapes, circular and square, and the entire perimeter of the weir or part of the perimeter is working as the weir crest length. The discharge passing over the unit length of the weir crest (q) is investigated and compared for the circular and square weirs of various crest lengths and positions. The results indicated that the discharge capacity of the circular weirs increases by a rate ranging between 7.5% and 15% more than that of the square weirs at the same head. Also, results indicated that the discharge coefficient of the circular weirs increases by a rate ranging between 9.3% and 10.3% more than that of the square weirs. This behavior can be attributed to the interference between the orthogonal water nappes at the corners of the square models. In addition, the flow direction has little effect on the discharge coefficient at small discharges, and this effect becomes more obvious at higher discharges. Additionally, the well-escape weirs of the upstream crest have a slightly higher discharge capacity than those of the downstream crest due to the effect of the approach velocity, which increases the water entrance velocity at the upstream crest. The results of flow patterns around the weir showed that the locations of maximum flow velocities (u, v, w) are mostly near the weir crest and depend entirely on the crest length and position.

Impact of different cephalometric skeletal configurations on anatomic midface parameters in adults

ObjectivesSkull morphology and growth patterns are essential for orthodontic treatment, impacting clinical decision making. We aimed to determine the association of different cephalometric skeletal configurations on midface parameters as measured in 3D CT datasets.Materials and methodsAfter sample size calculation, a total of 240 fully dentulous patients between 20 and 79 years of age (mean age: 42 ± 15), who had received a CT of the skull within the scope of trauma diagnosis or intracranial bleeding, were retrospectively selected. On the basis of cephalometric analysis, using MPR reconstructions, patients were subdivided into three different vertical skull configurations (brachyfacial, mesofacial, dolichofacial) and the respective skeletal Class I, II, and III relationships. Anatomic parameters were measured using a three-dimensional post-processing console: the thickness of the maxillary and palatine bones as well as the alveolar crest, maxillary body and sutural length, width and height of the hard palate, maxillary facial wall thickness, and masseter muscle thickness and length.ResultsIndividuals with brachyfacial configurations had a significantly increased palatal and alveolar ridge thicknesses compared to those with dolichofacial- or mesofacial configurations. Brachyfacial configurations presented a significantly increased length and thickness of the masseter muscle (4.599 cm; 1.526 cm) than mesofacial (4.431 cm; 1.466 cm) and dolichofacial configurations (4.405 cm; 1.397 cm) (p < 0.001). Individuals with a skeletal Class III had a significantly shorter palatal length (5.313 cm) than those with Class I (5.406 cm) and Class II (5.404 cm) (p < 0.01). Sutural length was also significantly shorter in Class III (p < 0.05).ConclusionsSkeletal configurations have an impact on parameters of the bony skull. Also, measurable adaptations of the muscular phenotype could result.Clinical relevanceThe association between viscerocranial morphology and midface anatomy might be beneficial for tailoring orthodontic appliances to individual anatomy and planning cortically anchored orthodontic appliances.

The hydraulic investigation of harmonic plan weirs

Existing dams and reservoirs need to be revised to meet safety standards. For the existing reservoirs where flood control is important and the maximum water level is limited, the best method to increase reservoir capacity is to build a labyrinth weir on the dam. In labyrinth weirs, the collision of two nappe flows produces nappe interference, and this reduces the weir performance. In this study, the semi-circle weirs are placed in an open channel harmonically to increase the efficiency of the labyrinth weirs to make the areas more efficient and increase the flow capacity because of the nappe interference and to ensure the flow moving perpendicular to the weir as possible. In the experimental study of the asymmetrically placed circular weirs, 3 different weir heights (P = 20 cm, 30 cm and 40 cm) and 3 different labyrinth cycle numbers (N = 2, N = 3 and N = 4) were used. As a result of the experiments, although there was a 13 % decrease in the discharge coefficients (Cd) compared to the linear weirs, it provided a 57 % increase in the net crest length (Lnet). Discharge coefficient (Cd) is decreased 3.4 %, as the number of cycles (N) increases. As the weir height (P) decreases, Cd increases 7.5 % due to the vacuum effect.

Multi-Sensor Observations Reveal Large-Amplitude Nonlinear Internal Waves in the Kara Gates, Arctic Ocean

We present multi-sensor measurements from satellites, unmanned aerial vehicle, marine radar, thermal profilers, and repeated conductivity–temperature–depth casts made in the Kara Gates strait connecting the Barents and the Kara Seas during spring tide in August 2021. Analysis of the field data during an 18-h period from four stations provides evidence that a complex sill in the Kara Gates is the site of regular production of intense large-amplitude nonlinear internal waves. Satellite data show a presence of a relatively warm northeastward surface current from the Barents Sea toward the Kara Sea attaining 0.8–0.9 m/s. Triangle-shaped measurements using three thermal profilers revealed pronounced vertical thermocline oscillations up to 40 m associated with propagation of short-period nonlinear internal waves of depression generated by stratified flow passing a system of shallow sills in the strait. The most intense waves were recorded during the ebb tide slackening and reversal when the background flow was predominantly supercritical. Observed internal waves had wavelengths of ~100 m and traveled northeastward with phase speeds of 0.8–0.9 m/s. The total internal wave energy per unit crest length for the largest waves was estimated to be equal to 1.0–1.8 MJ/m.

Geometric Modification of Piano Key Weirs to Enhance Hydraulic Performance and Discharge Capacity

The piano key (PK) weir is a cost-effective structure for flood discharge. Its typical layout comprises a rectangularly cranked crest in planform with up- and downstream overhangs. With the intention to enhance its hydraulic efficiency, the conventional weir is improved. The sloping floor of each key is modified with a downward semi-circle in the cross-section; each overhanging apex is thus assigned an elliptical crest. Thus, the developed crest length of the resulting weir becomes considerably extended. Experiments are performed to compare the hydraulic behaviors of the improved weir with a reference one. The models are 3D-printed to attain high manufacture precision. For the model dimensions chosen in the study, the developed crest is ~36% longer. The study demonstrates that the improvements in geometry lead to appreciably enhanced flow discharge capacity. Within the hydraulic range examined, the augment in flow discharge varies within a range from 30% to 53%. In terms of both discharge capacity and flow patterns, the improved weir clearly outperforms the conventional one. The elliptical overhang apexes noticeably extend the developed crest length. The streamlined upstream overhang without singularity and the lowered inlet key floor reduce the entrance energy loss and improve the inflow to the inlet key and the flow over the crest. The lowered floor also gives rise to extra water volume, which administers to the flow motion towards the crest. For the outlet key, its lowered floor facilitates the outflow and alleviates the liableness of local submergence at high discharges. If the footprint for spillway construction is limited or the increase in the reservoir water stage must be controlled, the use of a more effective PK weir for flood discharge has significant engineering implications.

Manifestation of internal waves in the Southern Caspian Sea using satellite imagery

Iran's South Caspian coast is an important agricultural hotspot and densely populated area that attracts about 20 million domestic tourists in summer. Therefore, not only the coastal area ecosystem of the South Caspian Sea (SCS) but also their marine ecosystem is exposed to different environmental pollution. The ecosystem of the SCS especially in the onshore area strongly affected by Internal Waves (IWs) dynamics. IWs can capture, concentrate and transport, floating plastic debris, larvae, contaminants, and toxic pollutants in this basin. Therefore, detecting and zoning the SCS for IWs is critical to the management and protection of this enclosed basin. Measured data obtained from CTD and satellite imagery archives from Landsat 7, 8, and Sentinel-2 have been used to analyze and manifest IWs. Analysis and comparison of different satellite images reveal that the maximum wavelength of the IWs packet was about 400 m with a crest length of 18,000 m. However, the minimum packet had a wavelength of about 20 m with a crest length of 360 m. Based on the occurrence of IWs extracted by edge-finding algorithms on satellite images, the SCS can be divided into six original zones. Four zones of them located near the coastal line where freshwater rivers discharge to the sea in the rainy season and two other zones are in the deep water, which form under the dominant sea surface wind regime and sharp changing of bathymetry.

An Engineering Geological Appraisal of the Leakage Problem in Dora-1 Earthen Dam, Tigray: Implications for its Stability

Leakage is one of the major problems facing the functionality and sustainability of dams. It occurs through the embankment body, reservoir, foundation, and abutments. This study was conducted to identify the main causes of the leakage problem at the Dora-1 dam, located in the northern part of Ethiopia. It is an earthfill dam with a height of 43.5 m, crest length of 454 m, and reservoir capacity of 4.67 million cubic meters. Part of the embankment body was wet and swampy up to 20 m high from the ground due to leaking water. Geological investigation, laboratory test of the construction materials (including grain size analysis, specific gravity and water absorption, Atterberg limit, free swell, dispersion, permeability, and shear strength), and electrical resistivity investigation were used to identify and pinpoint the possible causes of the leakage problem. Results of the study show that the favorable geological features responsible for the occurrence of leakage include: (a) geological contact between sandstone and moderately to highly weathered basalt unit at the left abutment, (b) the gravelly sand deposit at the central foundation and (c) dyke outcrop at the river course within the reservoir running in the upstream-downstream direction. Results of laboratory tests for clay core show medium to high compressibility, good to poor workability, and semi-pervious to impervious permeability when compacted. The water absorption and the percentage finer of the filter material don’t satisfy the filter criteria and the shell material was found to be semi-previous. The anomalous in the resistivity survey result confirms the situation. Slope stability analysis of the embankment showed instability conditions at full reservoir level. Close follow-up and a downstream stabilization structure, including rock and gravel support, were recommended.&#x0D; Construction material; Embankment dam; Site investigations; Ethiopia.

Internal Solitary Waves within the Cold Tongue of the Equatorial Pacific Generated by Buoyant Gravity Currents

Abstract The equatorial cold tongue in the Pacific Ocean has been intensely studied during the last decades as it plays an important role in air–sea interactions and climate issues. Recently, Warner et al. revealed gravity currents apparently originating in tropical instability waves. Both phenomena have strong dissipation rates and were considered to play a significant role in cascading energy from the mesoscale to smaller horizontal scales, as well as to vertical scales less than 1 m. Here, we present Sentinel-3 satellite observations of internal solitary waves (ISWs) in the Pacific cold tongue near the equator, in a zonal band stretching from 210° to 265°E, away from any steep bottom topography. Within this band these waves propagate in multiple directions. Some of the waves’ characteristics, such as the distance between wave crests, crest lengths, and time scales, are estimated from satellite observations. In total we identify 116 ISW trains during one full year (2020), with typical distances between crests of 1500 m and crest lengths of hundreds of kilometers. These ISW trains appear to be generated by buoyant gravity currents having sharp fronts detectable in thermal infrared satellite images. A 2D numerical model confirms that resonantly generated nonlinear internal waves with amplitudes of O(10) m may be continuously initiated at the fronts of advancing gravity currents. Significance Statement Satellite imagery reveals the repeated occurrence of internal solitary waves in the near-equatorial region of the east Pacific, despite the absence of topography. These waves appear to be resonantly generated over the sheared Equatorial Undercurrent by gravity currents that propagate as frontal zones of 1000-km scale tropical instability waves, providing a physical link with viscous mixing scales.

A Morphologic and Morphometric Study of the Vermian Fossa and Internal Occipital Crest in Adult Indian Human Skulls

Introduction: The inner surface of the squamous part of occipital bone shows a prominent internal occipital crest that descends and bifurcates close to foramen magnum to enclose a small depression called vermian fossa. It has been reported that the internal occipital crest and vermian fossa affect the dural venous sinuses close to it and influence the cerebrospinal fluid flow. Few studies have reported morphology the morphology and morphometric features of vermian fossa. There is a paucity of literature regarding the morphology and morphometry of the internal occipital crest. Hence, the present study evaluated the morphological and morphometric details of the vermian fossa and internal occipital crest. Objectives: To provide morphologic &amp; morphometric data of the vermian fossa and internal occipital crest in the Indian population. Materials and Methods: This was a cross-sectional study, with a sample size of 64, carried out for a period of three months in the Department of Anatomy. The fossa's morphometric dimensions and the vermian fossa's different shapes observed were documented. The internal occipital crest was observed for shape &amp; length. All data was tabulated, analyzed, and summarized using mean and standard deviation. Results: The vermian fossa was present in 56(82.35%) bones. The type 1 variety was observed in 48(70.6%), type 2 variety in 1 (1.1%) bone and type 3 - atypical variety in 10.3%. The mean length and width of the vermian fossa was 8.9 ±4.41 mm and 8.02±3.50 mm, respectively. The internal occipital crest was sharp in 37(54.4%) bones, rounded in 24(35.3%) bones and wide in 6(8.8%) bones and ill-defined in one bone. The mean length of the internal occipital crest from the internal occipital protuberance to the posterior margin of the foramen magnum was 4.16±0.56 cm. Conclusion: An accurate knowledge of morphology and morphometry of vermian fossa and internal occipital crest and their variations is of significance in diagnostic and therapeutic performance of clinicians and radiologists. Variations in normal anatomical features need to be explored. Hence, this is of importance to anatomists and morphologists. KEY WORDS: occipital crest, vermian fossa, morphology, morphometry, cerebellum.

Estimating discharge coefficient of triangular free overfall using the GMDH technique

Abstract Free overfalls are hydraulic structures used in flood control, water supply, irrigation, and flow measurements. The hydraulic systems of free overfall depend on rectangular end shape. The studies that dealt with triangular crest are few and almost non-existent. In this study, a triangular end-shape design uses multiple linear regression (MLR) and group method of data handling (GMDH) methods for four models with six sub-models. Then, 24 scenarios were chosen and compared. The discharge coefficient (Cd) of a free overfall with a triangular terminal was predicted using experimental data. The triangular end edge shape increased crest length, the discharge coefficient, and discharge passing over free overfall. To this goal, 180 triangular free fall tests were performed. Data were collected for two triangular free overfalls with an opposite flow direction with three angles 600, 750, and 900. Results of Cd acquired using the two ways discussed above show that the algorithm GMDH outperforms the other method. Values for the GMDH approach mod46 testing variables: RMSE, MARE, SI, R2, and NSE are 6.08 × 10−17, 2.65 × 10−17, 6.00 × 10−17, 100.00%, and 1.00, respectively, while these values for MLR are 0.06332, 0.05970, 0.06624, 15.431%, and −3.0419, respectively. The GMDH technique shows the best results concerning MLR and then chooses the best four scenarios from 24 with a Cd percentage error not exceeding ±2%.