Hydraulic Structures: Fourth Edition

3. From equation (4.44) for S/q1/50.1919 (0.16),

C0.72260.743 log 0.19190.18919%, ya0.320 m.

From equation (4.45) for S/q2/30.100.23 (outside experimental

limit),

C0.5027(0.10)0.3850.20721%, ya0.328 m.

The equivalent roughness k 2 ais obtained from (Section 8.2.2)



R

n

1/6

18 log

with

 0.16 104 m,

a3.423 104.

Thus a# /7, i.e. the flow regime is hydraulically rough with

k0.7 mm. (Note that kis smaller than the 1.2 mm applicable to

Anderson’s experiments; also, equation (4.44) underestimates Cby

about 0.1 for very low values of S/q1/5when compared with actual

experimental results.)

As explained in Section 4.7.3 in the above computations (1–3) the

uniform flow depth for the water component in the water–air

mixturey 0 should have been used instead of y 0. On the other hand

forCabout 0.3 the difference between these two values is negligible

(from Straub and Anderson y 0 /y 0 0.98).

4. From equation (4.52) with 14° (Stan0.25) C21%. As
   n^28 g/R1/3, for non-aerated flow 0.0191 and from equation (4.43)

a0.0191 (1 1.190.21^2 )0.0175.

From the Darcy–Weisbach equation y 0 ^2 R 0 Q^2 a/b^28 gS0.0125 and

y 0 0.25 m (giving y 0 /y 0 0.965 and ya0.25/(1 0.21)0.316 m.

The aerated flow velocity is V3.75/0.2515.0 m s^1 (14.48).

Using equation (4.53) C0.75(sin 14)0.7526%.

5. From equation (4.50), for K 2 q/b3.75 m s^1. By trial and error,
   V19.45 m s^1 (velocity of aerated flow).

c 1 0.006 1.1241.

Thusya2.124y 0 0.550 m; C 1 (0.259/0.550)53%.

ya



y 0

19.45^2



9.810.206

V^2



gR

(^11)

(^1)

0.16 104



7

11.6 106



(gRS)1/2

11.6v



U*

6 R



a /7

238 DAM OUTLET WORKS