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I. The River ChannelA. Basic Mechanics
1. Laminar Flow2. Turbulent Flow3. Reynolds Number
Re = driving forces = V D p = (velocity * depth * fluid density) resisting forces u (fluid viscosity)
laminar < 500 700 < turbulent \
I. The River ChannelB. Flow Equations and Resisting Forces
Discharge = velocity * depth * widthQ = V*A
1. Manning Equation
1.Manning Equation
v = R 2/3 S ½nWhere
v = average flow velocityr = hydraulic radiuss = channel slope (unitless)n = Manning roughness coefficient
R = A/P A = Area P = Wetted Perimeter
Q = A R 2/3 S ½
N
WhereQ = average flow dischargeA = area of channelR = hydraulic radiusS = channel slope (unitless)n = Manning roughness coefficient
R = A/P A = Area P = Wetted Perimeter
I. The River ChannelB. Flow Equations and Resisting Forces
1. Manning Equation2. Chezy Equation
V = C *(RS)1/2
II. Sediment in ChannelsA. Transportation1. Suspended load 2. Bedload3. Washload
B. Entrainment and ErosionC. Deposition
II. Sediment in ChannelsA. Transportation1. Suspended load 2. Bedload3. Washload
B. Entrainment and ErosionC. Deposition
“ a battle between velocity and gravity”
III. The Quasi-Equilibrium Condition A. Hydraulic Geometry
Q = V*AQ = V * w * d
w = aQb
d = cQ f
v = kQ m
Q W d V10.1 33.3 0.71 0.4311.3 31.5 0.67 0.54
15 38 0.79 0.528.9 38 0.94 0.8156.8 40.7 1.1 1.27106 29.1 2.14 1.7119 44.5 1.95 1.37125 42.5 1.58 1.86132 42 1.9 1.66133 30 2.08 2.13181 43 1.9 2.22201 43 2.04 2.29312 55 2.24 2.54494 70 6.04 1.17503 66 3.47 2.2629 73 3.7 2.33674 71 4.55 2.09
1100 72.5 4.97 3.061740 75 5.56 4.172930 215 3.38 4.04
Distance Downstream
y = 14.904x0.2375
y = 0.2754x0.395
y = 0.2448x0.3669
0
50
100
150
200
250
0 500 1000 1500 2000 2500 3000 3500
Q - Discharge
wid
th, d
epth
an
d v
elo
citi
es
y = 0.2754x0.395
y = 0.2448x0.3669
y = 14.904x0.2375
0.1
1
10
100
1000
1 10 100 1000 10000
Discharge (cfs)
wid
th,
dep
th a
nd
vel
oci
ty (
ft,s
)
W
D
V
III. The Quasi-Equilibrium ConditionC. Channel Shape ….in cross section:
F = 255M-1.08
Where F = width to depth ratio (W/D)M = % silt and clay in channel
IV. Channel Patterns
….in plan view (bird’s eye)
StraightMeanderingBraided
Transition between StraightAnd Meandering is whenSinuosity is 1.5
A few final words on stream form….
Why do channels take on a certain pattern?????
It’s primarily due to the relationship between slope and discharge(or velocity)
A few final words on stream form….
Why do channels take on a certain pattern?????
It’s primarily due to the relationship between slope and discharge(or velocity)
The ole’ Chezy Equ:V = C *(RS)1/2
V = C *(DS)1/2
or
A few final words on stream form….
V = C *(DS)1/2
It’s primarily due to the relationship between slope and discharge (or velocity)
The ole Chezy Equ:
V = velocityC = roughnessD = depth of flowS = slope of channel
V = C *(DS)1/2
V = velocityC = roughnessD = depth of flowS = slope of channel
The change in slope is a RESPONSE to changes in channel shape,NOT a cause of braiding
Increasing the slope of a stream DOES NOT cause it to braid.
V. Rivers, Equilibrium, and Time
the graded river: (page 227)“one in which, over a period of years, slope is delicately
adjusted to provide, with available discharge and with prevailing channel characteristics, just the velocity required for the transportation of the load supplied from the drainage basin. The graded stream is a system in equilibrium; its diagnostic characteristic is that any change in any of the controlling factors will cause a displacement of the equilibrium in a direction that will tend to absorb the effect of the change.” Mackin, 1948
the graded river: Lane Diagram
Factors affecting stream morphology
• Width• Depth• Slope• Velocity• Discharge• Flow resistance• Sediment size• Sediment load
Leopold et al (1964)
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
Increase in load ??? ???Decrease in load ??? ???Increase in discharge ??? ???Decrease in discharge ??? ???
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
Increase in load Aggradation increaseDecrease in loadIncrease in dischargeDecrease in discharge
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
Increase in load Aggradation increaseDecrease in load Degradation decreaseIncrease in dischargeDecrease in discharge
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
Increase in load Aggradation increaseDecrease in load Degradation decreaseIncrease in discharge Degradation decreaseDecrease in discharge
V. Rivers, Equilibrium, and Time
Responses from adjusting load and discharge…
ACTIVITY RESPONSE SLOPE
Increase in load Aggradation increaseDecrease in load Degradation decreaseIncrease in discharge Degradation decreaseDecrease in discharge Aggradation increase