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Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
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Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

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Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
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Rapidly Varying Flow01:24

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Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
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Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
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Uniform Depth Channel Flow: Problem Solving01:18

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
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Updated: Sep 19, 2025

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm
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Developing a novel hybrid model based on GRU deep neural network and Whale optimization algorithm for precise

Amin Gharehbaghi1, Redvan Ghasemlounia2, Farshad Ahmadi3

  • 1Department of Civil Engineering, Faculty of Engineering, Hasan Kalyoncu University, Şahinbey, Gaziantep, 27110, Turkey.

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Summary

A novel hybrid deep neural network (DNN) model, the 2GRU×-WOA, significantly improves monthly streamflow predictions by optimizing input variables and model parameters. This advanced model enhances accuracy for hydrological cycle assessments.

Keywords:
Chehel-Chai river’s streamflowGRU and Bi-GRU modelsMeta-heuristic Whale optimization algorithmNovel hybrid 2GRU×–WOA modelTLP parameter

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Area of Science:

  • Hydrology
  • Artificial Intelligence
  • Environmental Science

Background:

  • Streamflow is a critical indicator for assessing human and climate impacts on the hydrological cycle.
  • Accurate streamflow prediction is essential for water resource management and flood control.

Purpose of the Study:

  • To develop an innovative deep neural network (DNN) structure for enhanced mean monthly streamflow prediction.
  • To integrate a double Gated Recurrent Units (GRU) model with a whale optimization algorithm (WOA) for improved accuracy.

Main Methods:

  • A hybrid 2GRU×-WOA model was developed, incorporating a multiplication layer and meta-heuristic optimization.
  • Feature selection using Pearson's correlation coefficient (PCC) and Cosine Amplitude Sensitivity (CAS) identified precipitation (Pm) as the key input.
  • The model was optimized with specific parameters: tanh-softsign activation, 0.5 dropout rate, and 70 hidden neurons.

Main Results:

  • The hybrid 2GRU×-WOA model achieved superior performance with R2=0.79, NSE=0.76, MAE=0.21 (m3/s), MBE=-0.11 (m3/s), and RMSE=0.36 (m3/s).
  • Compared to benchmark GRU and Bi-GRU models, the hybrid model showed a 6.8% increase in R2 and a 20.4% reduction in RMSE.
  • Individual GRU and Bi-GRU models yielded lower performance metrics (e.g., R2 of 0.59 and 0.66, respectively).

Conclusions:

  • The proposed hybrid 2GRU×-WOA model offers a significant advancement in streamflow prediction accuracy.
  • This approach provides a robust tool for hydrological forecasting, aiding in better water resource management.
  • The study highlights the effectiveness of integrating deep learning with meta-heuristic algorithms for complex environmental modeling.