Great difference of flow depth and Manning's roughness coefficients in main channels and floodplains, generate a strong gradient of lateral velocity and hence, a lateral shear stress in the interface of the main channel and floodplain. This phenomenon increases the head loss in river system. Mathematical models which are currently used for water surface profile computations in rivers, e.g. HEC-RAS and MIKE11, neglect this mechanism. For taking into account this mechanism, the energy slope and energy correction factor should be modified in Gradually varied flow computations. In this paper, using exchange discharge method, the current procedure of Gradually varied flow computations were modified for compound channels. Comparison of this method and HEC-RAS results in an experimental flume with heterogeneous compound section in case of drawdown profile, M2, showed that the accuracy of these methods are 95 and 84.5%, respectively.

Toreducetheconstructioncostsofstilling basinsofhydraulic~umptype is sometimes,novelgeometriesaresometimes usedto adoptthe basinto the upstreamand downstreamsectionswithout any transition structures.Otherwise,any changesin thegeometryofthe basinwould causechangesin theconditionsandcharacteristicsofthe hydraulicjump. In this study,the effectsof variationin boththe sideslopesandthe divergingangleof a Graduallyexpandingstillingbasin with trapezoidal section on the jump condition were experimentally investigated. The experimental tests were conductedin a speciallydesignedmodelfora widerangeof sideslopesandlongitudinaldivergencesof the basinwalls. The important parameters of the jump, such as the length, sequent depth and the rate of energy loss were computed and compared to those in the normal jumps. Tests were conducted for three different side slopes (0.5: 1, I: 1, 1.5:1) and four diverging angle (3", 5", 7; 9") with the straight jump in the rectangular section and in the wide scope of decsent numbers (trom3 to 9). The results indicate that any decrease in the side wall slQPesfor a particular angle of divergence would cause a reduction in the sequent depth and an increase in the jump length and energy loss compared to the rectangular section on the same angle of divergence. It is also found that the longitudinal divergence of the side walls for a particular side slope will increase the stability of the jump within the stilling basin. It will also cause a reduction in the sequent depth and the jump length as well as an increase in energy loss of the jump, when compared to the straight jumps in either rectangular or trapezoidal sections.

In this research an Artificial Neural Network (ANN), with multilayer perception structure, was adapted to model conjugate depth and Gradually expanding jump length, which are especial but complex cases of hydraulic jumps. More than 3000 interpolated and experimental data on conjugate depths and jump lengths for both normal and Gradually expanding jumps were used. The data was due to rectangular and trapezoidal sections, for a wide range of divergent angles and side wall slope. In developing the ANN models, seventeen configurations, each having a different number of hidden layers and/or neurons, were investigated. The optimal models were capable of predicting conjugate depth and jump length for a wide range of conditions. In each case, the configuration attained highest R2 value was selected as the optimal model. For rectangular sections, the simplest ANN model had a 2-2-1 configuration, with one neuron in each of the two hidden layers, and R2=0.97 (for normal x section), and had a 4-1-1 configuration, with nine neurons in the hidden layer and R2=0.91 (for Gradually expanding x-section), respectively. The best ANN model for predicting respective jump lengths had 3-2-1 and 4-1-1 configurations with one and three neurons) in hidden layer(s), and R2= 0.99 and 0.94, respectively. For trapezoidal sections, the simplest ANN model had a 4-2-1 configuration, with nine neurons in each of the hidden layers and R2=0.99 (for normal x-section), and had a 5-2-1 configuration, with six neurons in each of the two hidden layers and R2=0.94 (for Gradually expanding x-section), respectively. The best ANN model for respective jump lengths had 42-1 and 5-2-1 configurations, with nine and six neurons in each of the two hidden layers, and R2=0.90 and 0.85, respectively. The high values obtained for R2 in all of the eight cases, suggest a close agreement between the Ann's output variable and the experimental data. The developed ANN models in this paper are, therefore, suitable for predicting Gradually expanding hydraulic jump characteristics, which require a large amount of repetitive computations, for both rectangular and trapezoidal sections often encountered in the design of stilling basins.

In this study, the effects of sharp-crested sill on the characteristics of hydraulic jump formed in a Gradually expanding stilling basin of rectangular cross section was investigated. The expansion of the basin is accomplished by increasing the bed width in the stream-wise direction. A total number of 228 tests were carried out for the range of initial Froude number from 3.1 to 10.3. Sills with various heights and different locations, relative to the jump toe, were installed in the basins with the diverging angles of 3, 5, and 9 degree. In all tests, the main characteristics of hydraulic jump including sequent depth ratio, relative length of jump and the relative energy loss were measured. The results indicate that installing sharp-crested sills have insignificant effect on the sequent depth ratio but may considerably decrease the length of jump. In addition, observations indicate that sills may improve general conditions and features of Gradually expanding hydraulic jump in a rectangular channel.

The length of the steady Gradually Varied Flow (G.V.F) profile in a circular gravity pipe section is computed using the Graphical Integration Method. The equations used for the solution are: a) the dynamic equation of Gradually Varied Flow in a prismatic channels, b) the hydraulic exponents M and N equation derived by Chow [2], and c) the Varied hydraulic exponents M (y/do) and N(y/do) equation modified by Zaghloul [15]. The results of the calculated G.V.F profile length using the modified hydraulic exponents M(y/do) and N(y/do) equation are closer to the G.V.F length calculated based on the exact formulation of the G.V.F dynamic equation. The percentage difference ranges from 0.67% to 8.72% for various bed slopes and G.V.F depth limits. The calculated G.V.F profile length using the Chow hydraulic exponents M and N resulted in wider values with percentage difference ranges from 0.16 to 25.59%. Hence, a remarkable improvement of the computation of G.V.F profile is achieved using the modified M(y/do) and N(y/do) hydraulic exponents.The unsteady Gradually Varied Flow wave propagation in circular gravity pipe section is simulated using the Explicit Method. The Extended Transport block (EXTRAN) of the latest Storm Water Management Model (PCSWMM2000) was used to route the wave through a circular gravity pipe section. The resulting routed hydrographs by the Explicit Method and the EXTRAN Block of the PCSWMM 2000, provided similar flow peak and lag time in both cases.A computer package was developed for the Steady G.V.F length calculation for gravity pipes using the Microsoft Excel spreadsheet. The results are plotted using the Excel graphics capabilities.A second computer package using Microsoft Excel was developed for the Unsteady G.V.F simulation based on the Explicit Method. The routed hydrographs arc plotted by the Excel graphics capabilities.The Excel packages for the Steady and Unsteady G.V.F are user friendly and are posted on the Internet Website location http://briefcase.yahoo.com/civil engineering2001.ARead me File is provided for each Excel package and is used as a users guide.

In the present study, the hydraulic characteristics of vertical drops with screens and the gradual wall expanding downstream using FLOW-3D software are investigated. For this purpose, two porosity ratios of the screens of 40 and 50%, 5 Gradually expanding with 3 vertical drop heights in the specified discharge range were used. It was found that the numerical results are closer to the experimental results with the RNG turbulence model than k-ε, . By increasing the drop height, the Δ, E/E0 due to the jet floor impact intensity increased and yp/P value decreased. The maximum Δ, E/E0 for 25 cm height was 51. 60% and the lowest for 15 cm was 44. 25%. For a constant drop height with increasing discharge, the Δ, E/E0 decreased and yp/P increased. The Gradually wall expanding causes turbulence on the edges and a non-uniform distribution of yd/P and by increasing yp/P and yd/P, it caused a 25% increase in Δ, E/E0. The presence of screens increased yp/P, yd/P, and Δ, E/E0 by 44%. The simultaneous use of Gradually walls expanding and screens caused a 46% increase in Δ, E/E0 and a decrease in yp/P and yd/P values. It was shown that the contribution of screens is greater than the Gradually wall expanding, with their simultaneous application increasing Δ, E/E0 up to 33. 5%.

Analysis of flow through rockfill materials is usually carried out by solving the differential equation which is a combination of nonlinear [i=mvn] and continuity equations. However, solving this differential equation either by means of finite difference method or similar procedures is relatively time consuming, and with uncertainty involved in water surface profile this becomes even more difficult. To analyze flow through rockfill materials an alternative method which is based on Gradually varied flow theory may be applied that is comparatively simpler and less time consuming. To apply this alternative method it is necessary to examine the validity of assumptions on which Gradually varied flow method are based. Moreover, the involved parameters in Gradually varied flow equation should be reverted to porous media condition. In this research by conducting a vast number of experiments on various types of materials the acceptability of assumptions of Gradually varied flow method for analysis of flow through coarse porous media is investigated and the effect of physical characters of porous medium such as void ratio, uniformity coefficient Cu, gradation coefficient Cc and viscosity of fluid as well as certain features of flow such as velocity and hydraulic gradient are also examined. Findings indicate that: 1). by accepting some degrees of discrepancies, one may use the Gradually varied flow method for analysis of flow through coarse porous media. 2). the permeability parameters of coarse porous media may be successfully related to the physical characters of granular materials. 3). A Comparison between observed and computed flow profiles through media indicates accuracy and applicability of equations that are derived by authors of this paper.

Background and Objectives Gradually varied flow is one of the common profiles of open channel flow which takes place in canals and natural conduits due to hydraulic structures and morphological causes. Spatial variations of flow characteristics is one of the most apparent properties of Gradually varied flow that its precise calculation through accurate solution of dynamic equation of Gradually varied flow has significant role. Three main approaches to solve dynamic equation of Gradually varied flow are analytical, numerical and graphical ones. Of these mentioned methods, direct integration of dynamic equation of Gradually varied flow is the most accurate method. Gaussian hyper-geometric functions (GHF), which has been considered in this research work, is one of the approaches to integrate directly of dynamic equation of Gradually varied flow. Creation of dimensionless form of dynamic equation of Gradually varied flow is the basis of the GHF method. This is done using normal depth of flow (yn-based method) or critical depth of flow (yc-based method). At the end of the paper, a comparison has been performed between GHF method and Rong-Kutta numeric method to predict GVF profile in a rectangular laboratory flume for three M1, S2 and C3 profiles. Methodology The GHF solver (F2 1(a, b; c; z)=Γ (c)Γ (a)Γ (b)Σ Γ (a+k)Γ (b+k)Γ (c+k)k! zk∞ k=0) has been implemented to integrate differential dynamic equation of GVF [dydx=So-Sfcosθ-α Q2TgA3]for five channel slops including Mild (M), Steep (S), Horizontal (H), Critical (C) and Adverse (A). Dimensionless form of GVF equation makes it easy to integrate using GHF solver. Due to the absence of normal depth for horizontal and adverse slopes, yc was used to produce dimensionless form of GVF equation for H and A slopes. Other three slopes were made dimensionless using yn. For the first scenario, two dimensionless parameters were defined as v=yyc and x#=xSc*yc. The correspondes parameters for the second scenario were u=yyn and x*=xSo*yn. The final integrated forms of the GVF equation include the hydraulic exponents as M and N which can be solved for certein values of M and N. To compar the results between numerical (Runge-Kutta 4th order method) and analytical (GHF) solvers, lobaratory GVF data measured from a rectangular flume of length 7 m, width 0. 1 m, height 0. 3 m and roughness 0. 011 were used. Three profiles as M1, S2 and C3 were formed experimentally to measure the GVF characteristics. Also, three performance assessment indices as RMSE, R2 and E were applied to compare the solvers accuracy. Findings Two analytical answers (overall 10 answers) were obtained to solve Gradually varied flow dynamic equation. The first group belongs to the channels of slope types namely M, S and C. The second one can be used for the slopes of types H and A. These two mentioned group answers should be used according to the profile name and corresponding zone. Regarding to the laboratory measured data of GVF profiles, results showed that application of GHF not only resolve discretization selection for numerical methods, but also predicts GVF profile characteristics more accurate than to the numerical Rong-Kutta 4th order solver. The amount of the (RMSE, R2, E) for the M1, S2 and C3 profiles for GHF were (0. 0173, 0. 9986, 1. 11), (0. 0167, 0. 9984, 1. 12) and (0. 0204, 0. 9988, 0. 985), respectively; while the corresponding values of numerical solver were calculated as (0. 0458, 0. 9864, 4. 05), (0. 0259, 0. 991, 2. 38) and (0. 0327, 0. 985, 3. 65). These values prove the superiority of GHF predictor. Conclusion Gradually varied flow profiles are common at the flow conduits with hydraulic structures. Predicting flow characteristics of GVF can be achievable through solving differential dynamic equation. In this paper, GHF was applied to solve the equation analytically. The obtained analytical answers can be used for all zones of five channel slope types.

This paper is devoted to study $\mathcal{I}$-convergent,$\mathcal{I-}$null, $\mathcal{I-}$bounded and bounded sequence spaces in gradual normed linear spaces, denoted by $c_{\| \cdot \|_G} ^\mathcal{I} ,c_{0 \| \cdot \|_G} ^\mathcal{I} ,\ell_{\infty \| \cdot \|_G} ^\mathcal{I}, \ell_{\infty \| \cdot\|_G}, m_{\| \cdot \|_G} ^\mathcal{I}$ and $m_{0 \| \cdot \|_G} ^\mathcal{I}$ respectively. We discussed some algebraic and topological properties of these classes. Also, we studied some inclusions involving these spaces.

In recent years, the use of nanoparticles in the field of medicine has attracted many attentions. The surface coating of nanoparticles by biocompatible polymers improves their bioavailability. Due to the compatibility of bio-polymers with the environment and human body, these materials are used as carrier agents. In this research, magnetic nanoparticles were synthesized by microwave and hydrothermal methods. The iron oxide nanoparticles (Fe3O4) were coated with polyvinyl alcohol (PVA) to prepare nanocomposite and load the drug (vitamin C) from the mechanical agitator. The nanoparticles crystal structure was studied using X-ray diffraction (XRD). The nanoparticles size was determined by scanning electron microscopy (SEM). Vibrating sample magnetometer (VSM) was used for magnetic analysis, and the purity of the material was determined by applying Fourier transform infrared spectrometer (FT-IR). Evaluation of drug release was investigated by ultra violet-visible (UV-Vis) spectroscopy.