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OPEN CHANNEL FLOW ANNOUNCEMENTS HW#7 assigned FLOW IN CHANNELS Flow in channels is different than overland flow Headwater watershed areas 1,000 mi 2 Small area floods / small river systems Flash floods
OPEN CHANNEL FLOW ANNOUNCEMENTS HW#7 assigned FLOW IN CHANNELS Flow in channels is different than overland flow Headwater watershed areas 1,000 mi 2 Small area floods / small river systems Flash floods of short duration Headwater watershed areas 1,000 mi 2 Flood controls are engineering controls Dams / channels / etc Channel flow equations apply to: Small creeks as well as large rivers Magnitude of flow is the only difference Equations and principles apply to both small and large channels TYPE OF STREAMS Ephemeral streams Only contain water when there is surface runoff Dry unless there is a rainfall event that produces SRO Intermittent streams Dry part of the year Flow when groundwater is high Flow when surface runoff occurs Perennial streams Flow throughout the year Groundwater provides baseflow during dry periods ORDER NUMBER (N) OF STREAMS System for classifying drainage networks 1 st order streams (n = 1) Smallest finger-tip tributaries 2 nd order streams (n = 2) When two 1 st order streams join 3 rd order streams ( n = 3) Etc When two 2 nd order stream join Useful only when n is proportional to channel: Dimensions Size of contributing watershed Stream discharge STREAM MORPHOLOGY Stream patterns and geometry influenced by: Geology Topography Size of contributing watershed Flow velocity Discharge Sediment transport Sediment particle distribution Channel geometry Other geomorphological controls STREAM MORPHOLOGY Streams attempt to be in equilibrium Equilibrium between sediment and deposition Channel patterns Sinuous Meandering : for a given discharge occur on smaller slopes Braided Sinuosity Ratio of stream length to valley length Sinuosity = 1 stream channel is straight 1 Sinuosity 1.5 channel is sinuous Sinuosity 1.5 channel is meandering Sinuosity 2.1 channel is tortuous meandering Stream Meandering STREAM FEATURES Inner side of stream curves Sand bar ridges point bars Where velocity is the slowest Outer side of stream curves Channel erosion (scour) deep pools Where velocity is the highest If stream equilibrium is not achieved: Scour on the outer bends continues Sinuosity increases Oxbow lakes may form Stream flow breaks through two bends to form a cutoff STREAM FEATURES Braided rivers No single, well defined channel Network of interconnecting streams A form of meandering Tend to be steeper, wider and shallower than undivided reaches carrying the same discharge A section of a channel is called a reach STREAM SCOUR Scour depends on: Soil / rock type in the channel Vegetation in the channel Flow rates in the channel Max permissible velocities for vegetated channels 8 ft/s Bermuda grass / 0-5% slope (SCS, 1984) Hydraulic behavior of vegetation will change as the flow rate increases Vegetation bends over and flattens out Resistance to flow is reduced increased flow velocity FLOW IN CHANNELS Function of: Precipitation Surface runoff Interflow Groundwater flow Pumped inflows / outflows Cross sectional geometry Bed slope Bed and side roughness Changes in shape Hydraulic control structures Sediment transport Channel stability Antecedent moisture conditions FLOW IN CHANNELS Turbulent flow Steep rocky areas Following storm events Steady uniform flow Depth of flow does not change quickly with time Hydraulic equations only apply to steady uniform flow OPEN CHANNEL HYDRAULICS Three basic relationships Continuity equation Energy equation Momentum equation CONTINUITY EQUATION Inflow 3 A 3a Change in Storage 3b Outflow 1 A 2 Inflow Outflow = Change in Storage Section AA Q 1 Q 2 = Change in storage rate CONTINUITY EQUATION FOR OPEN CHANNEL FLOW q = va, where: q = is the discharge (ft 3 /s) v = average velocity of the water (ft/s) a = cross-sectional area of the stream (ft 2 ) If q does not change along a channel reach, then: q = v 1 a 1 = v 2 a 2, where: 1 = upstream reach 2 = downstream reach MANNING S EQUATION FOR OPEN CHANNEL FLOW where: v K n 3 R 2 S K=constant, 1.49 for English units and 1.0 for SI units v = velocity in ft/s or m/s n = Manning s roughness coefficient of the channel S = channel bed slope (ft/ft) or (m/m) Change in elevation / length of stream reach Rise / run R = hydraulic radius of the channel R = A / P, where: A = cross-sectional area of the channel (ft 2 ) or (m2) P = wetted perimeter channel (ft) or (m) 1 2 Manning s Roughness Coef. (n) FACTORS AFFECTING MANNING S N A. Surface Roughness B. Vegetation C. Channel Irregularity D. Channel Alignment E. Silting and Scouring F. Obstruction G. Size and Shape of the Channel H. Stage and Discharge I. Seasonal Change J. Suspended Material and Bedload. FLOW IN COMPOUND CHANNELS Natural channels often have a main channel and an overbank section. Overbank Section Main Channel FLOW IN COMPOUND CHANNELS Most flow occurs in main channel; however during flood events overbank flows may occur. In this case the channel is broken into crosssectional parts and the sum of the flow is calculated for the various parts. FLOW IN COMPOUND CHANNELS V i 1.49 n i S 1/ 2 A i P i 2 3 n Q V i A i 1 In determining R only that part of the wetted perimeter in contact with an actual channel boundary is used. i ENERGY EQUATION (BERNOULLI S) v 2 p v 2 p 1 y z 1 2 y z 2 h γ 2g γ 2g elevation head L,1 2 velocity head pressure head Energy loss between sections 1 and 2 OPEN CHANNEL ENERGY EQUATION In open channel flow (as opposed to pipe flow) the free water surface is exposed to the atmosphere so that p/g is 0, leaving: v 2g v 2g y1 z h 1 y2 z2 L,1 2 v 2 1 2g h L1-2 y 1 v 2 2 2g y 2 z 1 z Datum 2 1 2 SPECIFIC ENERGY E A v 2 2g y Datum and channel bottom A v 2 2g y E (Eqn. 4.6) E is the specific energy. SPECIFIC ENERGY (CONT.) y Section AA q = vy Where q is the flow per unit width. Eqn. 4.6 becomes: 2 q 2gy 2 y E (Eqn. 4.8) SPECIFIC ENERGY DIAGRAMS y y 2 y c y 1 E c E o E *Note q is constant. CRITICAL DEPTH, Y C The depth of flow corresponding to the minimum E is the critical depth, y c y c 3 2 q g or v gy c 1 FROUDE NUMBER, F v gy c is known as the Froude Number, F If F = 1, y = y c and flow is critical. If F 1, y y c and flow is subcritical. If F 1, y y c and flow is supercritical. F is independent of the slope of the channel, y c dependent only on Q. FROUDE NUMBER F v gd h For non-rectangular channels d h is the hydraulic depth, defined as the area divided by the top width, t. d h = A/t. Table 4.9 contains the properties of typical nonrectangular channels. WHAT IS UNIFORM FLOW? If flow characteristics at a point are unchanging with time the flow is said to be steady. If flow properties are the same at every location along the channel, the flow is uniform. The energy line, water surface and channel bottom are all parallel in uniform flow. NATURAL CHANNELS In natural flow situations flow is generally nonsteady and non-uniform. In designing most channels steady, uniform flow is assumed with the channel design being based on some peak or maximum discharge.
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