Brownlie (1983) Bed-roughness Predictor
In sediment transport calculations it is important to link n-values to the bed
regime. This is particularly true when hydraulic conditions shift between upper
regime and lower regime flow.
Brownlie sought to reconstitute the discontinuity in the graph of hydraulic
radius versus velocity, Figure 2.4. (Brownlie 1983) In the process of his
research, Brownlie collected the known sediment data sets, 77 in all, containing
7027 data points. Of the total, 75 percent were from flume studies and 25 percent
from field tests. He used 22 of these data sets and demonstrated a significant
agreement with both field and laboratory data.
Brownlie's basic equations were modified for SAM to display bed roughness
as a coefficient times the grain roughness. Any consistent set of units are
applicable.
n = [Bedform Roughness] * [Strickler Grain Roughness]
Equation 2-18
The resulting form of the equations for lower and upper regime are:
LOWER REGIME FLOW:
0.1374
R
n = 1.6940
0.034
(
) 0.167
0.1112
0.1605
σ
S
Equation 2-19
d 50
d 50
UPPER REGIME FLOW:
0.0662
R
0.034 ( d 50 0.167
)
n = 1.0213
0.0395
0.1282
σ
S
Equation 2-20
d 50
where
d50 = the particle size for which 50% of the sediment mixture is
finer.
R = hydraulic radius of the bed portion of the cross section.
S = bed slope; probably the energy slope would be more
representative if flow is non-uniform.
σ = the geometric standard deviation of the sediment mixture, where
17
Chapter 2
Theoretical Basis for SAM.hyd Calculations
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