Manning model

|

107

Rodney J. Sobey

Lateral structure of uniform flow

Journal of Hydroinformatics

06.2

2004

of the depth-integrated flow together with the horizontal

information is provided by the present theory.

`

CHEZY AND MANNING FRICTION MODELS

Chezy model

`

The relationship between C and f is direct:

8g

g

f 82

e OE

(28)

or

.

f

e

|

Figure 3

Natural channel.

As f is dimensionless, the simplest approach would be to

retain the previous algorithm, with a prior translation

from C to f and a subsequent translation from f9 to C9.

From the Stage 1 algorithm, Dh = - 2.00 m, yL = 0 m,

yR = 100 m and A = 300.0 m2. From the Stage 2 algorithm,

e = 2.26 m2/sec and f9 = 0.0011. Figure 2(b) shows the

Manning model

qx(y) profile. The profile is symmetric, as expected. The

The changes are more fundamental for the Manning

near-bank gradients are significantly less steep than those

model. The cross-section-integrated n would be specified

that would characterize a turbulent boundary layer

in place of f and a depth-integrated n9 predicted in place of

between parallel plates. But this is a lateral profile of a

f9. SI units are assumed in the following discussion. For

depth-integrated flow, where the depth integration has

FSS (footsecondslug) units, n and n9 are replaced by

integrated over the boundary layer profile in the vertical.

n/1.49 and n9/1.49, respectively.

The mean flow velocity gradients near the bed would

Equation (14) becomes

be quite sharp. Figure 2(c) shows the equivalent lateral

profile of qx(y)/[h(y) + Dh], the depth-averaged velocity.

q2

d2qx

x

gdnS0 gn 2

0

Figure 3(a) is a natural channel of roughly similar

(29)

e

dy2

dn/3

7

width and cross-section area. The same S0, f and Q as for

the rectangular channel example are adopted.

and Equation (17) becomes

From

the

Stage

1

algorithm,

Dh = - 4.95 m,

yL = 45.65 m, yR = 96.79 m and A = 240.0 m2. From the

y

yR

q2

Q2

yR

dqx

2

*h

x

Stage 2 algorithm, e = 0.55 m /sec and f9 = 0.0021. Figure

2

4/3

gn

e

gn 2

gAS0

(30)

P

dy.

A7/3

h 7/3

dy

3(b) shows the qx(y) profile, and Figure 3(c) the qx(y)/

L

yL

[h(y) + Dh] profile. As a direct consequence of the irregu-

In Stage 1 of the algorithm, Equation (18) would become

lar bathymetry, the lateral flow profile is asymmetric.

A further application of such structured uniform flow

Q2

solutions would be in the prediction of the longitudinal

43

2

gAS0 gn

f Dh

(31)

7 3P

.

A

dispersion coefficient for contaminant transport in the

same channel. The TaylorElderFischer theory (Fischer

In Stage 2 of the algorithm, Equation (23) becomes

et al. 1979) requires knowledge of the lateral distribution