[L1] 1 Open-Channel Flow [L2] 1) Overview [L4] - Flow where the free surface of the fluid is in contact with the atmosphere [L5] * Refers to flow within a channel exposed to the atmosphere or liquid flow within a partially filled conduit. [L4] - Includes irrigation systems, sewer lines, drainage ditches, gutters, etc. [L2] 2) Characteristics of Open-Channel Flow [L4] - Velocity of Open-Channel Flow [L5] * In open channels, flow velocity is zero at the sides and bottom due to the no-slip condition. [L5] * For symmetrical cross-sections, it is maximum at the mid-plane of the free surface. [L4] - Critical Reynolds Number for Open-Channel Flow [L5] * Laminar Flow : Re <= 500 [L5] * Transitional Flow : 500 < Re < 2000 [L5] * Turbulent Flow : Re >= 2000 [L5] * The Reynolds number for open-channel flow is generally greater than 50,000. This means the flow is typically almost turbulent. [L5] * Rh : Hydraulic Radius [L1] 2 Optimal Hydraulic Cross-Section (Hydraulic Radius) [L2] 1) Definition of Optimal Hydraulic Cross-Section [L4] - A cross-section that has the maximum hydraulic radius or the minimum wetted perimeter for a given cross-sectional area. [L2] 2) Examples of Optimal Cross-Sections [L4] - Parameters that result in the minimum wetted perimeter and consequently minimum flow resistance for a given cross-sectional area. [L4] - The optimal hydraulic cross-section in an open channel is a semi-circle. [L4] - In a rectangular channel, the optimal hydraulic cross-section is y=b/2 [L4] - In a trapezoidal channel, the optimal hydraulic cross-section is half of a regular hexagon. [L1] 3 Specific Energy and Critical Depth [L2] 1) Specific Energy [L4] - The sum of pressure head and kinetic head of liquid in an open channel. [L5] * The height from the channel bottom to the energy line. [L5] * The specific energy of liquid in an open channel is the physical energy relative to the channel bottom. [L4] - Distribution of Specific Energy [L5] * Specific energy reaches a minimum value, Es min, which is called the critical point and is defined by critical depth and critical velocity. [L2] 2) Critical Depth [L4] - The location where specific energy is minimized. [L2] 3) Hydraulic Jump [L4] - A phenomenon where the water surface rises when the fluid flow velocity decreases.