As it has been assumed that α' and β' are constant across the river (for convenience), Equations
2.113 and 2.114 become:
2
α = α′ A 3 Vi2 ∆ Qi
Q i
and
β = β′ A2 Vi2 ∆ Qi
Q
i
With the values in Table 2.4
(138.2) (220.9)
2
α = 1.024
= 1.221
(152.4)
3
(138.2) (180.5)
β = 1.008
= 1.083
(152.4)
2
These values for α (1.22) and β (1.094) differ from unity by appreciable amounts. The difference
may be important in many river channel calculations. If no data are available, the assumptions that
α = 1.22 and β = 1.1 should be used for river channels.
2.14.2 PROBLEM 2 Velocity Profiles and Shear Stress
A velocity and discharge measurement is made on the Missouri River at Sioux City. The total
discharge is 923.1 cms. The average depth is 2.38 meters and the average velocity is 0.738 m/sec
in a vertical section at a point 244 meters from the right bank. The velocity measurements at
various distances from the bottom (y) are shown in Table 2.5.
Also during this measurement the slope of the energy grade line was observed as 0.000206 and
mm.
Table 2.5. Observed Velocity Data.
y
Observed Velocity
(m)
(m/sec)
0.152
0.518
0.305
0.633
0.457
0.701
0.762
0.762
1.07
0.838
1.37
0.884
1.68
0.945
1.70
0.945
2.29
0.991
2.71
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