At bankfull discharge conditions Q1 = 8000 cfs and the width of a sand-bed stream (Ds1 = 0.6

-4

mm) is W1 = 250 ft, the maximum flow depth is yo1 = 8 ft m, the slope is Sf1 = 2.5 x 10 , and

the maximum velocity is V1 = 5 ft/s.

(a) Estimate the width, W2, depth yo2, slope Sf2 and velocity V2 at the same station when the

discharge Q2 is 200 cfs if the cross-sectional geometry is unknown.

The at-a-station hydraulic geometry relationships (Table 5.3) can be used when no specific

field data is available.

For width:

0.26

0.26

Q

200

W2 = W1 2

= 250

= 96 ft

Q

8000

1

For depth:

0.40

0.40

Q

1

= y o1 2

=8

= 1.8 ft

y o2

Q

40

1

Slope is unchanged:

S f1 = S f2 = 2.5 x 10 -4

For velocity:

0.34

0.34

Q

1

V2 = V1 2

=5

= 1.4 ft / s

Q

40

1

(b) Using the same station as for part (a), estimate the width, W2. depth yo2, slope Sf2 and

velocity V2 in an upstream section of this stream if the bankfull discharge is 500 cfs and the

material upstream is sand (D50 = 0.6 mm)?

The "downstream" geometry relationships can be used in this case. Two types of relationships

are given in Table 5.3. The sand bed relationships are a function of discharge only, whereas

the gravel bed relationships are a function of both discharge and sediment size. Both methods

are compared in the following.

5.73

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