In analysis of flow through rockfill media, due to high velocity and Reynolds number, the flow is transformed to non-Darcy state. In a Darcian flow, due to the linear relationship between velocity and hydraulic gradient, analysis is made more easily. However, by increasing the flow velocity, the regime is diverted from Darcy law and becomes turbulent where its analysis is more complicated. At the present stage, there are no exact criteria to distinguish between Darcy and non-Darcy flow. Since the manning equation has a wide application in open channel flow, in the present paper the concept of Darcy's friction factor has been combined with manning's equation and a new form of equation has been obtained for analysis of flow through a rockfill media. In the process of investigation, two sets of laboratory data from the tests conducted on flow through unconfined and confined rockfill media were obtained and the analytical relationships were calibrated accordingly. Based on the analytical solution and laboratory data, for determination of manning's roughness coefficient (n), new relationships were developed. For this purpose, more than 150 laboratory data from flow through confined and unconfined flumes filled with rockfill materials were used. The results of the investigation have proved the validity of application of the manning equation in a fully rough flow.

Vegetation as one of the main effective factors in the flow resistance directly influence the flow velocity by increasing the surface roughness. The calculation of flow velocity in hydraulic, hydrology science and all water projects, particularly river engineering, flood control, also for hydraulic and hydrologic modeling is necessary. One of the methods used for determing the velocity of flow is using the manning equation. In this research, some field experiments have been carried out to simulate runoff flow on two slops in order to determine the effects of vegetation on manning roughness coefficient on the hillslope of Aghghala in Golestan province. These experiments have been done on two rectangular plots, with a width of 2 meters, length of 18 meters, on two different slops i.e.4.1, 12.9 percent. The runoff was generated by pumping water out of a reservoir. The experiments were done firstly with vegetation and then the vegetation was removed from the plots and the experiments were repeated. Totally, these experiments were repeated 20 times. The slope, vegetation percentage, flow discharge rate for the hillslope were measured. Then, in each repetition, the flow velocity was calculated and also the hydraulic radius in 6 sections were determined. The manning roughness coefficient, with vegetation and without vegetation, determined using the manning equation for the two hillslopes was 0.0557, 0.0510 for low slope hill and 0.0652, 0.0564 for the high slope hill. After the calculation of manning coefficient of all repetitions, theT test results showed that the vegetation can significantly increase the roughness coefficient. The structure of the field experiments as well as the fact that sheet flow runoff and unsubmerged vegetation being the focus of the study were new in this research and there is no enough knowledge on them.

The manning roughness coefficient is an important parameter in the design and evaluation of furrow irrigation. Despite its importance, estimation of this parameter for surface irrigation is very difficult, particularly in furrow irrigation. In this study, an EVALUE model was used to estimate the manning roughness coefficient in furrow irrigation. The model was based on volume balance and developed to estimate the manning roughness coefficient in surface irrigation. EVALUE also estimates both infiltration parameters of the modified Kostiakov branch function. The main input for EVALUE is depth of flow along the furrow at different times. Evaluation of this model was carried out by comparing simulated advance and resection phases using SIRMOD software based on the estimated parameters and the measured data. The estimated values of the manning roughness coefficient ranged from 0.02 to 0.102. This model was able to simulate the resection phase, which was more sensitive to the manning roughness coefficient, closely.

In the study of natural waterways, the use of formulas such as manning's equation is prevalent for analyzing flow structure characteristics. Typically, floodplains exhibit greater roughness compared to the main river channel, which results in higher flow velocities within the main channel. This difference in velocity can lead to increased sedimentation potential within the floodplains. Therefore, accurately determining manning's roughness coefficient for compound channels, particularly during flood events, is of significant interest to researchers. This study aims to model the manning roughness coefficient in compound channels with both converging and diverging floodplains using advanced soft computing techniques. These techniques include a multi-layer artificial neural network (MLPNN), Group Method of Data Handling (GMDH), and the Neuro-Fuzzy Group Method of Data Handling (NF-GMDH). For the analysis, a dataset from 196 laboratory experiments was used, which was divided into training and testing subsets. Input variables included parameters such as longitudinal slope (S_o), relative hydraulic radius (R_r), relative depth (D_r), relative dimension of flow aspects (δ^*), and the convergent or divergent angle (θ) of the floodplain. The relative manning roughness coefficient (n_r) was the output variable of interest. The results of the study showed that all the models performed well, with the MLPNN model achieving the highest accuracy, characterized by R² = 0.99, RMSE = 0.001, SI = 0.0015, and DDR = 0.0233 during the testing phase. Further analysis of the soft computing models indicated that the most critical parameters influencing the results were S_o, R_r, D_r, δ^*, and θ.

manning roughness coefficient is one of the most important parameters in designing water conveyance structures. Unsuitable selection of this coefficient brings up some mistakes. This research aims to present a method to determine the manning roughness coefficient based on a combination of optimization algorithm of simulated annealing (SA) with gradually varied flow equations. Therefore, in a lab rectangular flume of 12 m, 60 cm and 65 cm in length, width and height with fixed channel bed slope of 0.0002, nine series of water level profiles were carried out. Then, an objective function based on observed and calculated water level gradient was defined to decide on manning roughness coefficient while it was minimized with simulated annealing optimization method. The values of objective function parameters were discussed by sensitivity analysis and the most optimal objective function was obtained. To measure the accuracy of coefficient obtained, Statistics indices of R2, Root mean square error (RMSE), Mean bias error (MBE), d were used. The results showed that manning roughness coefficient has a great accuracy.

This study aimed to estimation of the manning roughness coefficient (n) in different phases and events of irrigation using empirical relations. For this purpose, six inflow rates in two flow categories, low and high, three consecutive irrigation events, advance and storage phases, two irrigation intervals and two types of soil texture were investigated. Next, the correlation between roughness and these parameters was investigated using Pearson and Kendall statistical tests. Then, using its results, regression equations were developed to estimate manning’s n in different irrigation phases. The results indicated that the advance time and the size of clods before irrigation had a high correlation and the slope, initial soil moisture and the size of clods after irrigation had a low correlation with the manning’s n data in the whole irrigation event. The roughness coefficient of the advance phase also had the highest correlation with the advance time. The highest and lowest correlation coefficients between the parameters and roughness coefficient of the storage phase were related to advance time and inflow rate with values of 0.65 and -0.31, respectively, which shows high correlation and direct relationship between advance time and roughness and weak correlation and inverse relationship between flow rate and roughness. The average values of R2, RMSE, and NRMSE indices in the provided relationships were 0.87, 0.014, and 26.97%, respectively, which indicated the appropriate accuracy of these relationships. Finally, it was suggested to conduct similar studies in different field and hydraulic conditions so that the presented relations are more comprehensive and can be recommended in other fields since the development of such relations can increase the speed of roughness estimation in different phases and the ease of using it.

Surface irrigation is still main irrigation system in agricultural land, so it is necessary to finding a solution for improving these systems. manning roughness coefficient and infiltration parameters are the most important parameters in evaluation of surface irrigation systems. Infiltration parameters play an essential role in the evaluation and design of irrigation systems; therefore, it is necessary to estimate these coefficients, accurately The purpose of this study was to estimate infiltration parameters and manning roughness coefficient in continuous and cutback flows during the first three irrigation events using INFILT, SIPAR_ID and EVALUE models. The results showed that the average relative error percentage in the INFILT, SIPAR_ID and EVALUE models were 16. 6, 5. 2 and 11. 2, respectively, and the maximum errors were 1. 6, 0. 7, and 1. 1 m3, respectively. The SIPAR_ID model has less error than the other two models. These models also had higher accuracy in estimating infiltration in the border irrigation than furrow irrigation. The US Soil Conservation Service (SCS) also proposed a manning roughness coefficient for fallow furrows in the first irrigation 0. 04, which is very different from the estimated values of the SIPAR_ID model from 0. 038 to 0. 09.

Resistance to surface flow such as manning's and Darcy-Weisbach rouphness coefficients were an important input for estimating soil erosion by soil erosion process models. Also, it is very important for designing and implementing soil and water conservation practices. The objective of present research was predicting manning's and Darcy-Weisbach rouphness coefficients in surface of a loess soil under different rock fragment covers. For this porpose, a flume was used with 6 m length, 0.5 m width and 3% slope. The treatments included rock fragment cover (0, 10, 20 and 30%) and three levels of flow discharges (3, 6 and 9 lit. min-1). The results showed that manning's and Darcy-Weisbach rouphness coefficients increased as exponential with increasing rock fragment cover. Darcy-Weisbach coefficient increased 84.3, 83.8 and 85.7% with an increase rock fragment cover from 0 to 30% at 3, 6 and 9 lit min-1 flow discharges, respectively, and manning's rouphness coefficient increased 96.9, 96.7 and 97.4% at mentioned flow discharges. Rouphness coefficients decreased as exponential (R2=0.99) with increasing flow velocity at a rock fragment cover. Also, (8/f)0.5 increased as logarithmic with increasing relative submergence. Generally, results of this study showed that rouphness coefficients not only were dependent on size and shape rock fragment cover but also, were influenced by factors such as flow rate, depth and velocity and also, rock fragment cover percentage.

Various methods have been developed to estimate the manning roughness coefficient, of which the inverse method is widely used. This study aimed to estimate the inverse of manning roughness coefficient using the WinSRFR model and estimating infiltration parameters of Kostiakov-Lewis equation in furrow irrigation and to investigate their variations in different irrigation events. For this purpose, two inflow discharges (average 0. 27 and 0. 53 liters per second), two irrigation cycles (5 and 10 days), two fields with different soil texture (E and F) in three irrigation events (first to third) were considered in three replications. Model error in estimating advance and recession time, and volume of infiltrated water was investigated using statistical indices including RE, RMSE and NRMSE. The values of these indices in estimating the advance time in the field E were 0. 44%, 0. 21 min and 1. 11% in the total three irrigation events, respectively. Also, the values of these indices were 1. 58%, 5. 25 min and 2. 78% in the recession time and 0. 59%, 5. 5 liters and 0. 50% in the volume of infiltrated water, respectively. There was less error in estimating the advance and recession time in the field F which showed the excellent accuracy of the inverse estimation method using the WinSRFR model in determining the manning roughness coefficient. The results also showed that in the field E, the minimum and maximum values of manning roughness coefficient were estimated as 0. 017 and 0. 34 and on average 0. 075 in the total three irrigation events, respectively. In the field F, the minimum, maximum and the average values of manning roughness coefficient in three irrigation events were 0. 015 and 0. 09 and 0. 041, respectively.

Accurate estimation of mean velocity and discharge of open channels is one of important goals in hydraulic knowledge. Application of manning equation is one of the methods with abundant use for mean velocity calculation. Application of this equation in several cross sections such as circular section is associated with error.In this study, effective hydraulic radius is defined based on cross section shape in Cartesian coordinates. In this definition, the effect of water surface roughness is applied in calculations with respect to a weight factor greater than one. By application of effective hydraulic radius in manning equation for circular cross section a good accordance was observed between calculated and existed experimental results. Root square means error of relative computational velocity and discharge from the conventional and effective hydraulic radius toward experimental data are 0.14904, 0.08125 and 0.01113, 0.00042, respectively. Results showed that application of effective hydraulic radius has a significant effect on increasing the accuracy of manning equation compared with conventional hydraulic radius.