The mean values of exponents b, f, m, j, z, and y as reported by Leopold et al. (1964) are
given in Table 5.2. These values are based on an extensive analysis of stream data in the
United States and are stream specific.
Table 5.2. At-A-Station and Downstream Hydraulic Geometry Relationships.
Average At-A-Station Relations
b
f
m
j
z
y
Average values Midwestern United States
.26
.40
.34
2.5
Brandywine Creek, PA
.04
.41
.55
2.2
.05
-.2
Ephemeral Streams in Semiarid U.S.
.29
.36
.34
Average of 158 Gaging Stations in U.S.
.12
.45
.43
Ten Gaging Stations on Rhine River
.13
.41
.43
Average Downstream Relations
(bank-full or mean annual flow)
b
f
m
j
z
y
Average values Midwestern United States
.5
.4
.1
.8
-.49
Brandywine Creek, PA
.42
.45
.05
-1.07
-.28
Ephemeral Streams in Semiarid U.S.
.5
.3
.2
1.3
-.95
-.3
Appalachian Streams
.55
.36
.09
In Table 5.3, derived hydraulic geometry relations for conditions at-a-station (variable discharge
frequency) and in the downstream direction on the same stream at bankfull discharge (or
constant frequency) are given. Note: the term "downstream" implies any other location along
the channel, either upstream or downstream from a selected station. Bray (1982) and Julien
and Simons (1984) determined that bed material size is an important variable in hydraulic
geometry relations in alluvial gravel streams. Their relations for non-cohesive gravel-bed rivers
in the downstream direction at bankfull discharge (or constant frequency) are also given in
Table 5.3. Applications of these relationships are illustrated in Section 5.9 (Problems 5 and 6).
Table 5.3. Derived At-A-Station and Downstream Geometry Relationships.
(1)
(1)
(2)
At-A-Station
Downstream
Downstream
y o ≈ Q 0.40
y o ≈ Q b.46
0
y o ≈ Q b.40
0
-0
W ≈ Q 0.26
W ≈ Q 0.46
W ≈ Qb.53 D50.33
0
V ≈ Q 0.34
V ≈ Q b.08
0
V ≈ Qb.07 D0033
0
.
5
-
-
+1
S f ≈ Q 0.00
S f ≈ Qb0.46
S f ≈ Qb0.4 D 50.00
(1)
Sand bed
(2)
Gravel bed
5.26
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