(e) Summary
The average shear stress on the boundary from (a) is 4.805 newtons per square meter. This is the
average stress on the entire boundary (bed and banks). The shear stress computed using velocity
is the local shear stress on the bed where the velocity profile was taken. This local shear stress is
calculated as 5.11 in (b), 4.37 in (c), and 3.98 in (d). Normally the use of the two point velocity
equation with the velocities close to the bed is the more accurate, however, very accurate velocity
measurements are required. For this example, the value from the two velocity method appears to
be low. For wide channels the centerline local shear stress on the bed should generally not be
lower than the average shear stress on the boundary (i.e., the value of 4.805 newtons per square
meter).
2.14.3 PROBLEM 3 Superelevation in Bends
Calculate the superelevation of the water surface in a river bend given the velocity profile from
Table 2.4. The river radius of curvature ri is measured equal to 106.7 meters and the outer radius
of curvature ro is 156.4 meters. The detailed calculations based on Equation 2.158 are presented in
Table 2.7.
Table 2.7. Detailed Computation of Superelevation in Bends.
Vi2
∆Z i =
∆ri (m)
rI (m)
VI (m/s)
∆rI (m)
gri
0.61
107.3
0.00
.0000
1.82
109.1
0.300
.0002
2.44
111.6
.165
.0001
2.44
114.0
.195
.0001
2.44
116.4
.732
.0011
2.44
118.9
.966
.0020
2.44
121.3
1.23
.0031
2.44
123.7
1.24
.0031
2.44
126.2
1.15
.0026
2.44
128.6
1.14
.0025
2.44
131.1
1.15
.0025
2.44
133.5
1.44
.0038
2.44
136.0
1.31
.0031
2.44
138.4
1.49
.0040
2.44
140.9
1.41
.0035
2.44
143.3
1.32
.0030
2.44
145.8
1.19
.0024
2.44
148.2
.945
.0015
2.44
150.6
.921
.0014
2.44
153.1
.515
.0004
1.68
154.8
0.00
.0000
0.76
155.6
0.00
.0000
0.0404 m
Total ∆Z
2.74