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Chapter 6Open Channel Hydraulics1ObjectivesUpon completing this chapter, you should be able to:Compute the slope of a channelCompute the cross-sectional area, wetted perimeter, and hydraulic radius of a channelIdentify normal depth in a channelIdentify and compute critical depth in a channel2Fundamental ConceptsPrismatic channelMaintains constant slope and shapeEssential elements: channel bottom, water surface and energy grade line (EGL) above water surfaceHGL coincides with water surface

34The hydraulic grade line (HGL) and the energy grade line (EGL) for free discharge from a reservoir through a horizontal pipe with a diffuser.Hydraulic grade line (HGL), P/g + z The line that represents the sum of the static pressure and the elevation heads. Energy grade line (EGL), P/g + V2/2g + z The line that represents the total head of the fluid. Dynamic head, V2/2g The difference between the heights of EGL and HGL.

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Figure Concrete channel with trapezoidal cross section. Delmar, Cengage Learning 2014.5Fundamental ConceptsSlopeVertical fall divided by horizontal run

Or expressed by % i.e. 0.050= 5%

6Depth of flow D or d or yDistance from channel bottom to water surfaceCross-sectional area of flowArea of a cross-section of flowing water (a) see figure above

Fundamental Concepts (contd.)Wetted perimeter (p)Distance along the channel cross section that is in contact with the flowing water i.e the sum of the distance AB+BC+CDHydraulic radiusChannel cross-sectional area divided by wetted perimeter

8Fundamental Concepts (contd.)Hydraulic radius (contd.)

a = cross-sectional areap = wetted perimeter

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Types of ChannelsMany different shapes and sizesSlope, shape or alignment changes:NonprismaticFlow characteristics are affected: chnages from uniform to varied flow11

Typical channel cross-section shapes.Delmar, Cengage Learning 2014.12

Velocity distributions in rectangular and trapezoidal channels. Values are multiples of average velocity. Delmar, Cengage Learning 2014.Maximum velocity just below free surface in center of channel13Normal Depth

14Critical DepthSpecific energy (E=D+v2/2g)Critical depthMinimum value of ETheoretical conceptDepends on channel slope and flow Q

15Critical Depth (contd.)a = cross-sectional areaT = top width of channelQ = flow rateg = acceleration due to gravity

16Figure 6-6: Specific energy diagram. Delmar, Cengage Learning 2014.

17Critical Depth (contd.)Subcritical flowDepths greater than critical depthTranquil flowSupercritical flowDepths less than critical depthMore rapid flow18Critical Depth (contd.)Critical velocityVelocity of water at critical depthCritical slopeChannel slope that causes normal depth to coincide with critical depth19Critical Depth (contd.)Froude numberUsed to distinguish between supercritical and subcritical flow

F = Froude numberv = average velocityD = flow depthg = acceleration due to gravity

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Figure 6-7: Channel transition. Subcritical flow transitions to supercritical flow by passing through critical depth.Delmar, Cengage Learning 2014.21