Assume Cd0.65; thus H 10 3/(20.65 1
9
.6
2
)2.69 m, and !
1 (0.015557.5)/2.690.67. 57.52.6960.19y 1 102 /(19.60.67^2 y 12 );
y 1 0.436 m. Fr^21 123;y 2 6.62 m; (7.53.7)/6.621.69#1.19. The
basin designed for the maximum discharge is more than adequate for
lower discharges.
From equation (5.10) the stilling basin length LK(11.65 0.873);
forFr 1 9
5
.7
5
9.78 and K4.5;L4.510.77748.49 m50 m.
From equation (5.14) for V 1 25/0.87328.63 m s^1 andy 1 0.873 m,k y ̄
0.05 6.045.
Thus, theoretically, there is no cavitation danger, even for the maximum
discharge.
From equation (5.15) for d 90 118 mm, y 0 6.416 m, and H*
55.032 6.41648.616 m, ys0.55[648.6160.25 25 0.5(6.416/118)1/3 6.416]
13 m. As S 50 #10 m, this equation is not really applicable and the
computed scour depth is far too high. A more realistic result is about 50%
of this value, i.e. about 6.5 m. This maximum scour is likely to occur at a
distanceL 6 6.590 m from the toe of the dam and is thus harmless
for the dam, but requires suitable bank protection.
If a flip bucket were used the probable required depth of the plunge
pool would, from equation (5.16b), beys1.5 25 0.648.6160.115.25 m.Thusys15.25 6.4169 m below river bed level. (This erosion would,
however, very probably be closer to the toe of the dam unless a chute,
diverging the flow from the dam, were used.)
From equation (5.17) for 14° 1 24°,ys6(25^2 /9.8)1/3tan 1 , i.e.
6.0ys10.6 m; this agrees reasonably well with the previous result of
ys9 m. However, equations (5.16d) and (5.16e) give bigger results (16 m
and 12 m).References
Annandale, G.W. (1995) Erodibility. Journal of Hydraulic Research, IAHR, 33,
No. 4: 471–94.
–––– (2006) Scour Technology: Mechanics and Engineering Practice, McGraw-Hill,
New York.
Basco, D.R. (1969) Trends in Baffled Hydraulic Jump Stilling Basin Design of the
Corps of Engineers since 1947, Miscellaneous Paper H-69-1, US Army Engi-
neers Waterways Experimental Station, Vicksburg.
Boes, R.M. and Hager, W.H. (2003) Hydraulic design of stepped spillways, Journal
of Hydraulic Engineering ASCE, 129, No. 9: 671–9.(10 3 y 1 )19.62
0.0528.63^2V^21
2 gp 0
g