and

β = β A2 Vi2 ∆ Qi

'

Q

i

With the values in Table 2.8

(1,485) (85,490)

2

α = 1.024

= 1.247

(5,369)

3

(1,485) (21,070)

β = 1.008

= 1.094

(5,369)

2

These values for α (1.247) 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 = 1.25 and β = 1.1 should be used for river channels.

A velocity and discharge measurement is made on the Missouri River at Sioux City, Iowa. The total

discharge is 32,600 cfs. The average depth is 7.80 feet and the average velocity is 2.42 ft/sec in a

vertical section at a point 800 feet from the right bank. The velocity measurements at various

distances from the bottom (y) are shown in Table 2.9.

Table 2.9. Observed Velocity Data.

y

Observed Velocity

(ft)

(ft/sec)

0.5

1.70

1.0

2.08

1.5

2.30

2.5

2.50

3.5

2.75

4.5

2.90

5.5

3.10

6.25

3.10

7.5

3.25

Also during this measurement the slope of the energy grade line was observed as 0.000206 and

The log and power function velocity distribution functions will be used to obtain a mathematical

description of the velocity profile.

(a) Logarithmic Velocity Distribution Equation

2.81

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