Hydraulic Geometry
Brian Bledsoe
Department of Civil Engineering
Colorado State University
Regime Theory / Hydraulic Geometry
(e.g. Lacey 1929, Leopold and Maddock 1953)
Channel parameters may be sufficiently described
with power functions utilizing Q as the sole
independent variable
w  aQ
b
h  cQ
f
v  kQ
Q  whv  (a  c  k )Q
m
b f m
ack  b  f  m 1
Hydraulic Geometry - Exponents
At-a-Station
b  0.1  0.2
Downstream
b  0.5
f  0.4
f  0.33  0.40
m  0.4  0.5
m  0.10  0.17
b is width, f is depth, and m is velocity
Downstream hydraulic geometry
The Basic Issue
Predicting channel width / depth in the
context of heterogeneous bed and bank
conditions
w, h, S, v
• Continuity
• Friction loss
• Sediment transport or incipient motion
• ???
Three General Approaches
Empirical
• Regime Equations / Hydraulic Geometry
•
•
Lacey, Simons and Albertson, Blench, USACE, Julien and
Wargadalem, many others including “regional curves”
Context-specific - require judgment / caution
“Rational / Analytical”
• Copeland Method (now in HEC-RAS)
• Lateral Momentum Transfer - Parker
• Millar
Extremal / Variational / Thermodynamic
• Minimum S, VS, Fr, dVS/dw
• Maximum f, Qs, Qs/S
Hydraulic Geometry Approach
in Stable Channel Design
• Rooted in regime theory of Anglo-Indian
engineers
• Canal design
• Low sediment loads
• Low variability in Q
• Does not directly consider sediment load (slope
equations are dangerous for sand bed channels)
• Neglects energy principles and time scales of
different adjustment directions
• Fluvial system is actually discontinuous,
e.g. tributaries, variability in coefficients
Downstream hydraulic geometry
equations for width provide an
important channel design and
analysis tool
Depth, velocity, and slope
equations are less reliable
Some Factors Affecting a
w  aQ
•
•
•
•
•
•
•
•
•
•
0.5
Vegetation / soils / light interactions
Root reinforcement and depth / bank height
Woody debris inputs and bank roughness
Bank cohesion / stratigraphy / drainage
Freeze / thaw
Sediment load
Flow regime (e.g. elevation of veg. on banks)
Return period of extremes vs. recovery time
Lateral vs. vertical adjustability / time
Historical context
Downstream Hydraulic Geometry
and Boundary Sediments
Schumm (1960)
w
1.08
 255M
h
Richards (1982)
w
0.15 1.20
 800Q B
h
Hey and Thorne (1986)
All Veg. Types
Bankfull Width (m)
100
y = 3.663x0.4468
10
1
1
10
100
Bankfull Discharge (cms)
1000
Hey and Thorne (1986)
Separate Veg. Types
Bankfull Width (m)
100
10
Veg Type 1
y = 5.1864x0.4468
Veg Type 2
y = 3.2647x0.5015
Veg Type 3
y = 1.969x0.5702
Veg Type 4
y = 1.9209x0.5444
1
1
10
100
Bankfull Discharge (cms)
1000
Downstream Hydraulic Geometry
and Vegetation
w  aQ
0.5
Hey and Thorne (1986)
•
•
•
•
Grassy banks  a = 4.33
1-5% tree / shrub  a = 3.33
5-50% tree / shrub  a = 2.73
> 50% tree / shrub  a = 2.34
Andrews (1984)
•
•
Thin  a = 4.3
Thick  a = 3.6
Width (m)
10
1
Davies-Colley forest
Davies-Colley pasture
Hession et al. forest
Hession et al. non-forest
1
10
Drainage Area (km 2)
Hey and
Thorne (1986)
and Charlton
et al. (1978)
data
100
100
Width (m)
Davies-Colley
(1997) and
Hession et al.
(2003) data
10
Hey and Thorne thick
Hey and Thorne thin
Charlton et al thick
Charlton et al thin
10
100
Qbf (m 3/s)
Log Channel Width
Grass
Forest
10 -100 km2
Log Watershed Area
% Silt and Clay
Root Density (ml l-1)
Values of a in w = aQ0.5
Unit
System
Very
Wide
Average
Width
Very
Narrow
English
2.7
2.1
1.3
SI
4.9
3.8
2.3
Vegetation Density, Stiffness, Root Reinforcement
Bank Cohesion
Suspended Sediment Load
Bed Material Size / Braiding Risk
?
Summary
 Downstream
hydraulic geometry
relationships for width can provide a useful,
additional relationship in channel design
 Selection of the coefficient a is complicated
and requires consideration of many factors
 Vegetation effects tend to override
sedimentary effects
 Processes are scale-dependent?