The Structure of Filter Curve and Methods of Its Approximation. Part 3. Equations for Filter Curve Approximation

The paper describes the structure of the filtration curve built in a wide range of variation of filtration rates. A detailed description of the mechanism of occurrence and development of the inertial component of the filtration flow structure is given. Equations are presented that can be used to approximate the filtration curve. A modified equation is proposed that provides a smooth transition from laminar to turbulent filtration without discontinuities of the velocity and pressure fields, which can be used when calculating both one-dimensional and spatial filtration flow.

The throughput of filtering outlet works (filter spillways) on rockfill dams with screen

Introduction. The most economical type of spillway for rockfill dams with reinforced concrete screens are filtering outlet works (filter spillways). Deals with the main issue of designing filtering outlet works - assessment of their throughput on the basis of analytical solutions of turbulent filtration through the water intake of the filtering outlet works in rockfill dams with reinforced concrete screen. The objectives of the work are: • analysis of water flow in the filtering outlet work on the rockfill dam with reinforced concrete screen; • derivation of formulas for determining the throughput of the filtering outlet works on rockfill dams with reinforced concrete screen; • comparison of the results of determining the throughput of the filtering outlet works in the application of the proposed formulas; recommendations on the use of the proposed formulas. Materials and methods. The analysis of the water flow in the filtering outlet works and the derivation of the formulas is based on the adoption of three assumptions on the trajectory of the elementary streams of water in the filtering outlet works: on a circular trajectory, with a vertical fall, along the free fall trajectory with a gradient equal to one. Calculations of the throughput of the filtering outlet works were performed for the design of the filtering outlet works, patented by the author. Results. The results of calculations according to the proposed formulas showed a significant difference depending on the accepted hypothesis about the nature of the movement of the filtration flow in the body of the rockfill dam. It is revealed that the most acceptable calculations are based on the formula derived under the assumption of the flow motion along the free fall trajectory with a gradient equal to one. Conclusions. The results of the study made it possible to formulate the following recommendations: 1. The capacity of the filtering outlet works is recommended to be determined by the formula derived in the assumption of the flow motion along the free fall trajectory with a gradient equal to one, as more appropriate to the hydraulics of the filter spillways on the rockfill dams with the screen. 2. Further study of the hydraulics of the filter outlets works of various designs and analysis of their impact on the design of rockfill dams would allow for a more substantiated to determine their ability to pass the flood and recommend them for implementation.