CE 1501 Selected Topic: Open Channel Flow Reading: Munson, et al., Chapter 10

CE 1502 Introduction Open channel flow - flow of a liquid in a channel (or conduit) that is not completely filled Main driving force is gravity; pressure force is only hydrostatic Applications –river/stream flow –flow in canals, ditches, gutters, sewers –ocean waves, tidal effects –roadway, parking lot runoff

CE 1503 General Characteristics Free surface represents an additional degree of freedom (and complexity) compared to pipe flows New parameter: fluid depth (y) which may vary with time (t) and distance along channel (x) Classifications based on depth –Uniform flow (UF): constant depth, or dy/dx = 0 –Gradually varying flow (GVF), dy/dx << 1 –Rapidly varying flow (RVF), dy/dx  1

CE 1504 General Characteristics Classification based on flow condition –Laminar: Re  500 –Transitional: 500  Re  12,500 –Turbulent: Re  12,500 –where

CE 1505 Surface Waves Waves can occur when the channel boundaries are suddenly perturbed Waves travel due to hydrostatic pressures differences Small amplitude wave speed –Solitary waves: –Sinusoidal waves:

CE 1506 Froude Number Froude number is the ratio of fluid speed to wave speed: –Froude number determines the surface characteristics of open channel flow Subcritical flow: Fr < 1 Critical flow: Fr = 1 Supercritical flow: Fr > 1

CE 1507 Channel Depth for GVF Channel depth variation for steady, gradually varying flow (GVF): –If S f > S 0 and Fr < 1, channel depth will increase –If S f < S 0 and Fr < 1, channel depth will decrease –See Table 10.2 for all possibilities and classifications

CE 1508 Manning Equation For uniform channel flow (UF), the average velocity is given by the Manning equation: –where  = unit conversion constant n = Manning resistance coefficient (see Table 10.1)

CE 1509 Hydraulic Jump The hydraulic jump is an example of a rapidly varying flow (RVF), where a shallow high-speed flow suddenly changes to a deeper, low-speed flow The jump occurs due to a conflict between upstream influences (supercritical flow, Fr > 1) and downstream influences (subcritical flow, Fr < 1) The energy loss of a hydraulic jump is useful in spillway design