(e) Summary

The average shear stress on the boundary from (a) is 0.10 pound per square foot. 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 0.108 in (b), 0.094 in (c), 0.084, 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 for 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 0.10

pounds per square foot.

Calculate the superelevation of the water surface in a river bend given the velocity profile from

Table 2.8. The river inner radius of curvature ri is measured equal to 350 feet and the outer radius

of curvature ro is 513 feet. The detailed calculations based on Equation 2.158 are presented in

Table 2.11.

Table 2.11. Detailed Computation of Superelevation in Bends.

Vi2

∆Z i =

∆ri (ft)

rI (ft)

VI (ft/s)

∆rI (ft)

gri

2.0

352

0.00

.0000

6.0

358

0.98

.0005

8.0

366

0.54

.0002

8.0

374

0.64

.0003

8.0

382

2.40

.0037

8.0

390

3.17

.0064

8.0

398

4.02

.0101

8.0

406

4.06

.0101

8.0

414

3.78

.0086

8.0

422

3.74

.0082

8.0

430

3.78

.0083

8.0

438

4.71

.0126

8.0

446

4.30

.0103

8.0

454

4.90

.0131

8.0

462

4.63

.0115

8.0

470

4.32

.0099

8.0

473

3.89

.0079

8.0

486

3.10

.0049

8.0

494

3.02

.0046

7.0

502

1.69

.0014

5.5

507

0.00

.0000

2.5

512

0.00

.0000

0.1330 ft

Total ∆Z

2.84

Integrated Publishing, Inc. |