(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).

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

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